Systems and methods for creating and using combined predictive models to control hvac equipment

ABSTRACT

A heating, ventilation, or air conditioning (HVAC) system for a building includes HVAC equipment, a controller, and a predictive modeling system. The HVAC equipment are operable to affect an environmental condition in the building. The controller is configured to determine an operating point for the HVAC equipment and to operate the HVAC equipment at the operating point. The predictive modeling system includes a plurality of HVAC component models and one or more prediction combiners. The HVAC component models are configured to generate a plurality of component model predictions based on the operating point. The prediction combiners are configured to combine the plurality of component model predictions to form a combined model prediction. The controller is configured to use the combined model prediction to optimize the operating point and to operate the HVAC equipment at the optimized operating point.

BACKGROUND

The present disclosure relates generally to predictive modeling systemsfor HVAC equipment and more particularly to a predictive modeling systemwhich combines the output of multiple predictive models to form acombined model prediction.

Modern energy conservation measures (ECM) include optimizing thedispatch of a central energy facility to use equipment at optimal timesof the day when efficiencies are higher, combined with adding thermalenergy storage to reduce the peak energy demand during the day. In orderto verify the effectiveness of an ECM, a baseline model is typicallycreated to find the initial cost of running the central energy facility.This cost is then compared to the cost of an optimized plant with newequipment added, and the capital savings is the difference between thesenumbers. Performance contracts rely on the ability to accurately createthe baseline model, as well as the projected savings.

Equipment models can be used to optimize the performance of the centralenergy facility. This optimization be performed in two ways: (1) as aplanning tool to run what if scenarios for capacity planning to see whatwould happen under different conditions and (2) as a real timeoperational tool to optimize the current running conditions. Both ofthese scenarios can use HVAC equipment models to predict powerconsumption and maintain flow, temperature, power, and pressure loadbalances.

Existing predictive modeling systems use a single model to predict theperformance of HVAC equipment under various scenarios. Efforts toimprove model prediction accuracy in the HVAC domain have focused ontrying to find a best fitting and generalizable model that works on awide variety of HVAC equipment of a particular type (e.g., ageneralizable chiller model). Although generalizable models performadequately under most operating conditions, no predictive model isperfect, no matter how complex. Accordingly, even the best predictivemodels can lack accuracy under some operating conditions. It would bedesirable to predict HVAC equipment performance in a manner thatovercomes the disadvantages associated with existing predictive modelingsystems.

SUMMARY

One implementation of the present disclosure is a heating, ventilation,or air conditioning (HVAC) system for a building. The HVAC systemincludes HVAC equipment, a controller, and a predictive modeling system.The HVAC equipment are operable to affect an environmental condition inthe building. The controller is configured to determine an operatingpoint for the HVAC equipment and to operate the HVAC equipment at theoperating point. The predictive modeling system includes a plurality ofHVAC component models and one or more prediction combiners. The HVACcomponent models are configured to generate a plurality of componentmodel predictions based on the operating point. Each of the componentmodel predictions is generated by one of the HVAC component models andincludes a predicted value of a performance variable indicating apredicted performance of the HVAC equipment at the operating point. Theprediction combiners are configured to combine the plurality ofcomponent model predictions to form a combined model prediction. Thecombined model prediction includes another predicted value of theperformance variable. The controller is configured to use the combinedmodel prediction to optimize the operating point and to operate the HVACequipment at the optimized operating point.

In some embodiments, the operating point is a setpoint for the HVACequipment and the performance variable indicates a predicted powerconsumption of the HVAC equipment at the setpoint.

In some embodiments, the HVAC system includes one or more sensorsconfigured to measure one or more measured variables associated with theHVAC equipment. The HVAC component models can be configured to generatethe component model predictions as a function of the measured variables.

In some embodiments, each of the HVAC component models has a differentfunctional form and uses a different mathematical relationship togenerate the corresponding component model prediction.

In some embodiments, the prediction combiners include an equal weightingcombiner configured to generate the combined model prediction bycalculating an average of the component model predictions.

In some embodiments, the prediction combiners include a varianceweighting combiner configured to identify a variance associated witheach of the component model predictions, assign a weight to each of thecomponent model predictions based on the variance associated therewith,and generate the combined model prediction by calculating a weightedaverage of the component model predictions using the assigned weights.

In some embodiments, the prediction combiners comprise a trimmed meancombiner configured to create an initial set of the component modelpredictions, identify one or more highest values of the component modelpredictions and one or more lowest values of the component modelpredictions create a filtered subset of the component model predictionsby removing the identified component model predictions from the initialset, and generate the combined model prediction by calculating anaverage of the component model predictions in the filtered subset.

In some embodiments, the trimmed mean combiner is configured to use avariance weighting technique to calculate the average of the componentmodel predictions in the filtered subset. The variance weightingtechnique can include identifying a variance associated with each of thecomponent model predictions in the filtered subset, assigning a weightto each of the component model predictions based on the varianceassociated therewith, and generating the combined model prediction bycalculating a weighted average of the component model predictions in thefiltered subset using the assigned weights.

In some embodiments, the HVAC system includes a model evaluatorconfigured to calculate a score for each of the prediction combiners bycomparing the combined model predictions generated by each of theprediction combiners to actual values of the performance variable. TheHVAC system can further include a combiner selector configured use thecalculated scores to select one of the prediction combiners. In someembodiments, the predictive modeling system is configured to use theselected prediction combiner to generate the combined model prediction.

Another implementation of the present disclosure is a method forcontrolling HVAC equipment. The method includes determining an operatingpoint for the HVAC equipment and generating a plurality of componentmodel predictions based on the operating point. Each of the componentmodel predictions includes a predicted value of a performance variableindicating a predicted performance of the HVAC equipment at theoperating point. The method further includes combining the plurality ofcomponent model predictions to form a combined model prediction. Thecombined model prediction includes another predicted value of theperformance variable. The method further includes using the combinedmodel prediction to optimize the operating point and operating the HVACequipment at the optimized operating point. Operating the HVAC equipmentaffects an environmental condition in a building.

In some embodiments, the operating point is a setpoint for the HVACequipment and the performance variable indicates a predicted powerconsumption of the HVAC equipment at the setpoint.

In some embodiments, the method includes measuring one or more measuredvariables associated with the HVAC equipment using one or more sensors.The component model predictions can be generated as a function of themeasured variables.

In some embodiments, each of the component model predictions isgenerated using a different HVAC component model. In some embodiments,each of the HVAC component models has a different functional form anduses a different mathematical relationship to generate the correspondingcomponent model prediction.

In some embodiments, combining the plurality of component modelpredictions to form the combined model prediction includes calculatingan average of the component model predictions.

In some embodiments, combining the plurality of component modelpredictions to form the combined model prediction includes identifying avariance associated with each of the component model predictions,assigning a weight to each of the component model predictions based onthe variance associated therewith, and generating the combined modelprediction by calculating a weighted average of the component modelpredictions using the assigned weights.

In some embodiments, combining the plurality of component modelpredictions to form the combined model prediction includes creating aninitial set of the component model predictions, identifying one or morehighest values of the component model predictions and one or more lowestvalues of the component model predictions, creating a filtered subset ofthe component model predictions by removing the identified componentmodel predictions from the initial set, and generating the combinedmodel prediction by calculating an average of the component modelpredictions in the filtered subset.

In some embodiments, a variance weighting technique is used to calculatethe average of the component model predictions in the filtered subset.The variance weighting technique can include identifying a varianceassociated with each of the component model predictions in the filteredsubset, assigning a weight to each of the component model predictionsbased on the variance associated therewith, and generating the combinedmodel prediction by calculating a weighted average of the componentmodel predictions in the filtered subset using the assigned weights.

In some embodiments, the method includes calculating a score for each ofthe prediction combiners by comparing the combined model predictions toactual values of the performance variable, selecting one of theprediction combiners based on the calculated scores, and generating thecombined model prediction using the selected prediction combiner.

Another implementation of the present disclosure is a system forcontrolling HVAC equipment. The system includes a plurality of HVACcomponent models configured to generate a plurality of component modelpredictions based on an operating point for HVAC equipment. Each of thecomponent model predictions is generated by one of the HVAC componentmodels and includes a predicted value of a performance variableindicating a predicted performance of the HVAC equipment at theoperating point. The system further includes one or more predictioncombiners configured to combine the plurality of component modelpredictions to form a combined model prediction. The combined modelprediction includes another predicted value of the performance variable.The system further includes a controller configured to use the combinedmodel prediction to optimize the operating point and to operate the HVACequipment at the optimized operating point. Operating the HVAC equipmentaffects an environmental condition in a building.

In some embodiments, the operating point is a setpoint for the HVACequipment and the performance variable indicates a predicted powerconsumption of the HVAC equipment at the setpoint.

Another implementation of the present disclosure is another a heating,ventilation, or air conditioning (HVAC) system for a building. The HVACsystem includes HVAC equipment operable to affect a temperature of thebuilding, a plurality of zone temperature models, one or more predictioncombiners, and a temperature controller. The zone temperature models areconfigured to generate a plurality of zone temperature predictions. Eachof the zone temperature predictions is generated by one of the zonetemperature models and includes a predicted value of the temperature ofthe building. The prediction combiners are configured to combine theplurality of zone temperature predictions to form a combined modelprediction. The combined model prediction includes another predictedvalue of the temperature of the building. The temperature controller isconfigured to use the combined model prediction to generate controlsignals for the HVAC equipment and to operate the HVAC equipmentaccording to the control signals.

In some embodiments, the system includes one or more sensors configuredto measure the temperature of the building. The zone temperature modelscan be configured to generate the zone temperature predictions as afunction of the measured temperature of the building and the controlsignals for the HVAC equipment.

Another implementation of the present disclosure is a heating,ventilation, or air conditioning (HVAC) system for a building. The HVACsystem includes HVAC equipment operable to affect a temperature of thebuilding, a plurality of models, one or more estimate combiners, and acontroller. The plurality of models are configured to estimate aplurality of values for a variable of interest in the HVAC system. Eachof the plurality of values is estimated by one of the plurality ofmodels. The estimate combiners are configured to combine the pluralityof estimated values to form a combined model estimate. The combinedmodel estimate includes another value of the variable of interest. Thecontroller is configured to use the combined model estimate to generatecontrol signals for the HVAC equipment and to operate the HVAC equipmentaccording to the control signals.

In some embodiments, the system includes one or more sensors configuredto measure one or more predictor variables. The plurality of models canbe configured to estimate the variable of interest as a function of themeasured predictor variables.

In some embodiments, the variable of interest is a building energy load.Each of the plurality of models can be configured to estimate a valuefor the building energy load at each of a plurality of times within atime period. The predictor variables can include one or more variablesthat affect the building energy load during the time period.

Those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a building equipped with a HVAC system, accordingto an exemplary embodiment.

FIG. 2 is a schematic of a central plant that includes a plurality ofsubplants which may be used to provide heating and/or cooling to thebuilding of FIG. 1, according to an exemplary embodiment.

FIG. 3 is a block diagram of a central plant system including a centralplant controller configured to manage the plurality of subplants of FIG.2, according to an exemplary embodiment.

FIG. 4 is a block diagram illustrating a portion of the central plantsystem of FIG. 3 in greater detail and showing a predictive modelingsystem configured to predict the performance of HVAC equipment,according to an exemplary embodiment.

FIG. 5 is a block diagram illustrating the predictive modeling system ofFIG. 4 in greater detail, according to an exemplary embodiment.

FIG. 6 is a schematic diagram of a chiller which is a type of HVACequipment for which performance can be predictive by the predictivemodeling system of FIG. 4, according to an exemplary embodiment.

FIG. 7 is a set of graphs illustrating a sliding window and iterativeprediction technique which can be used by the predictive modeling systemof FIG. 4, according to an exemplary embodiment.

FIG. 8 is flowchart of a process for controlling HVAC equipment whichcan be performed by the predictive modeling system of FIG. 4, accordingto an exemplary embodiment.

FIG. 9 is a flowchart of a process for evaluating model performancewhich can be performed by the predictive modeling system of FIG. 4,according to an exemplary embodiment.

FIG. 10 is a block diagram of a temperature control system which can usecomponents of the predictive modeling system of FIG. 4 to generatecontrol signals for HVAC equipment and control the temperature of abuilding, according to an exemplary embodiment.

FIG. 11 is a block diagram illustrating the flow of information betweena load estimator and a central plant controller which may be used tocontrol the central plant of FIG. 2, according to an exemplaryembodiment.

FIG. 12 is a block diagram illustrating the load estimator of FIG. 11 ingreater detail, according to an exemplary embodiment.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, systems and methods for creating andusing combined predictive models to control HVAC equipment are shown,according to various exemplary embodiments. Predictive models for HVACequipment can include any of a variety of models that characterize theperformance of the HVAC equipment. Throughout this disclosure, the terms“predictive model” and “equipment model” are used interchangeably.Equipment models can include power consumption models that can be usedto predict the power consumption of individual HVAC devices at variousoperating points. In some embodiments, equipment models can be used topredict various output variables (e.g., coefficient of performance,power consumption, etc.) of HVAC equipment as a function of themonitored variables and/or operating points.

In some embodiments, the equipment models define power consumption as afunction of equipment load and/or equipment setpoints. For example, anequipment model for a chiller may define the power consumption of thechiller as a function of cold water production and/or chiller loadsetpoints. In general, an equipment model for a particular HVAC devicemay define the relationship between the inputs to the HVAC device andthe outputs of the HVAC device. Equipment models can be used to predictan amount of input resources (e.g., electricity, water, natural gas,etc.) required to produce a desired amount of an output resource (e.g.,chilled water, hot water, electricity, etc.). Equipment models can beused to predict the power consumption of various devices of HVACequipment that will result from the on/off decisions and setpoints forthe HVAC equipment.

Equipment models can be used to optimize the operation of HVACequipment. For example, a central plant controller can use equipmentmodels in a real-time operational tool to optimize the current runningconditions of a physical plant. Equipment models can also be used by aplanning tool to operate a simulated plant under various hypotheticalscenarios to evaluate system performance under different sets ofconditions. The simulated plant can be adjusted to reflect plannedequipment purchases, installation of energy-efficient equipment, orother planned changes to allow the central plant optimizer to runvarious hypothetical scenarios before the changes are actually made tothe physical plant.

A predictive modeling system can use multiple equipment models for thesame predicted variable to generate multiple component modelpredictions. The predictive modeling system can then combine thecomponent model predictions for a given predicted variable to form acombined model prediction. The predictive modeling system can use any ofa variety of techniques to combine the component model predictions. Forexample, the predictive modeling system can use equal weighting,principal components, trimmed means, constrained or unconstrainedregression, artificial neural networks, variance weighting, ensemblemachine learning techniques (e.g., boosting, bagging, etc.), or anyother combination technique to generate a combined model prediction frommultiple component model predictions.

Combining multiple component model predictions to form a combined modelprediction has several advantages. For example, different componentmodels may use different input variables to predict the same outputvariable. This results in diversity of model inputs when the componentmodel predictions are combined, which can increase the accuracy of thecombined model prediction. Additionally, a diversity of component modeltypes can improve the accuracy of the combined model prediction incircumstances when specific types of component models may lack accuracy.For example, some component model types may be more accurate than othersat predicting chiller power consumption under high load conditions, butless accurate than the others at predicting chiller power consumptionunder low load conditions.

The existence of multiple different component model types increases theprobability that not all of the component models will lack accuracyunder the same set of conditions. Furthermore, using multiple differentcomponent models to predict the same variable allows for outlierpredictions to be identified and removed from the set of predictionsbefore combination. This can also increase the accuracy of the combinedmodel prediction by pruning outlier predictions. Additional features andadvantages of the predictive modeling system are described in greaterdetail below.

Building HVAC System

Referring now to FIG. 1, a perspective view of a building 10 is shown.Building 10 is served by a building automation system (BAS). A BAS is,in general, a system of devices configured to control, monitor, andmanage equipment in or around a building or building area. A BAS caninclude, for example, a HVAC system, a security system, a lightingsystem, a fire alerting system, any other system that is capable ofmanaging building functions or devices, or any combination thereof.

The BAS that serves building 10 includes an HVAC system 100. HVAC system100 may include a plurality of HVAC devices (e.g., heaters, chillers,air handling units, pumps, fans, thermal energy storage, etc.)configured to provide heating, cooling, ventilation, or other servicesfor building 10. For example, HVAC system 100 is shown to include awaterside system 120 and an airside system 130. Waterside system 120 mayprovide a heated or chilled fluid to an air handling unit of airsidesystem 130. Airside system 130 may use the heated or chilled fluid toheat or cool an airflow provided to building 10. In some embodiments,waterside system 120 is replaced with a central energy plant such ascentral plant 200, described with reference to FIG. 2.

Still referring to FIG. 1, HVAC system 100 is shown to include a chiller102, a boiler 104, and a rooftop air handling unit (AHU) 106. Watersidesystem 120 may use boiler 104 and chiller 102 to heat or cool a workingfluid (e.g., water, glycol, etc.) and may circulate the working fluid toAHU 106. In various embodiments, the HVAC devices of waterside system120 may be located in or around building 10 (as shown in FIG. 1) or atan offsite location such as a central plant (e.g., a chiller plant, asteam plant, a heat plant, etc.). The working fluid may be heated inboiler 104 or cooled in chiller 102, depending on whether heating orcooling is required in building 10. Boiler 104 may add heat to thecirculated fluid, for example, by burning a combustible material (e.g.,natural gas) or using an electric heating element. Chiller 102 may placethe circulated fluid in a heat exchange relationship with another fluid(e.g., a refrigerant) in a heat exchanger (e.g., an evaporator) toabsorb heat from the circulated fluid. The working fluid from chiller102 and/or boiler 104 may be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship withan airflow passing through AHU 106 (e.g., via one or more stages ofcooling coils and/or heating coils). The airflow may be, for example,outside air, return air from within building 10, or a combination ofboth. AHU 106 may transfer heat between the airflow and the workingfluid to provide heating or cooling for the airflow. For example, AHU106 may include one or more fans or blowers configured to pass theairflow over or through a heat exchanger containing the working fluid.The working fluid may then return to chiller 102 or boiler 104 viapiping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e.,the supply airflow) to building 10 via air supply ducts 112 and mayprovide return air from building 10 to AHU 106 via air return ducts 114.In some embodiments, airside system 130 includes multiple variable airvolume (VAV) units 116. For example, airside system 130 is shown toinclude a separate VAV unit 116 on each floor or zone of building 10.VAV units 116 may include dampers or other flow control elements thatcan be operated to control an amount of the supply airflow provided toindividual zones of building 10. In other embodiments, airside system130 delivers the supply airflow into one or more zones of building 10(e.g., via air supply ducts 112) without using intermediate VAV units116 or other flow control elements. AHU 106 may include various sensors(e.g., temperature sensors, pressure sensors, etc.) configured tomeasure attributes of the supply airflow. AHU 106 may receive input fromsensors located within AHU 106 and/or within the building zone and mayadjust the flow rate, temperature, or other attributes of the supplyairflow through AHU 106 to achieve setpoint conditions for the buildingzone.

Central Plant and Control System

Referring now to FIG. 2, a block diagram of a central plant 200 isshown, according to an exemplary embodiment. In brief overview, centralplant 200 may include various types of equipment configured to serve thethermal energy loads of a building or campus (i.e., a system ofbuildings). For example, central plant 200 may include heaters,chillers, heat recovery chillers, cooling towers, or other types ofequipment configured to serve the heating and/or cooling loads of abuilding or campus. Central plant 200 may consume resources from autility (e.g., electricity, water, natural gas, etc.) to heat or cool aworking fluid that is circulated to one or more buildings or stored forlater use (e.g., in thermal energy storage tanks) to provide heating orcooling for the buildings. In various embodiments, central plant 200 maysupplement or replace waterside system 120 in building 10 or may beimplemented separate from building 10 (e.g., at an offsite location).

Central plant 200 is shown to include a plurality of subplants 202-212including a heater subplant 202, a heat recovery chiller subplant 204, achiller subplant 206, a cooling tower subplant 208, a hot thermal energystorage (TES) subplant 210, and a cold thermal energy storage (TES)subplant 212. Subplants 202-212 consume resources from utilities toserve the thermal energy loads (e.g., hot water, cold water, heating,cooling, etc.) of a building or campus. For example, heater subplant 202may be configured to heat water in a hot water loop 214 that circulatesthe hot water between heater subplant 202 and building 10. Chillersubplant 206 may be configured to chill water in a cold water loop 216that circulates the cold water between chiller subplant 206 building 10.Heat recovery chiller subplant 204 may be configured to transfer heatfrom cold water loop 216 to hot water loop 214 to provide additionalheating for the hot water and additional cooling for the cold water.Condenser water loop 218 may absorb heat from the cold water in chillersubplant 206 and reject the absorbed heat in cooling tower subplant 208or transfer the absorbed heat to hot water loop 214. Hot TES subplant210 and cold TES subplant 212 may store hot and cold thermal energy,respectively, for subsequent use.

Hot water loop 214 and cold water loop 216 may deliver the heated and/orchilled water to air handlers located on the rooftop of building 10(e.g., AHU 106) or to individual floors or zones of building 10 (e.g.,VAV units 116). The air handlers push air past heat exchangers (e.g.,heating coils or cooling coils) through which the water flows to provideheating or cooling for the air. The heated or cooled air may bedelivered to individual zones of building 10 to serve the thermal energyloads of building 10. The water then returns to subplants 202-212 toreceive further heating or cooling.

Although subplants 202-212 are shown and described as heating andcooling water for circulation to a building, it is understood that anyother type of working fluid (e.g., glycol, CO₂, etc.) may be used inplace of or in addition to water to serve the thermal energy loads. Inother embodiments, subplants 202-212 may provide heating and/or coolingdirectly to the building or campus without requiring an intermediateheat transfer fluid. These and other variations to central plant 200 arewithin the teachings of the present invention.

Each of subplants 202-212 may include a variety of equipment configuredto facilitate the functions of the subplant. For example, heatersubplant 202 is shown to include a plurality of heating elements 220(e.g., boilers, electric heaters, etc.) configured to add heat to thehot water in hot water loop 214. Heater subplant 202 is also shown toinclude several pumps 222 and 224 configured to circulate the hot waterin hot water loop 214 and to control the flow rate of the hot waterthrough individual heating elements 220. Chiller subplant 206 is shownto include a plurality of chillers 232 configured to remove heat fromthe cold water in cold water loop 216. Chiller subplant 206 is alsoshown to include several pumps 234 and 236 configured to circulate thecold water in cold water loop 216 and to control the flow rate of thecold water through individual chillers 232.

Heat recovery chiller subplant 204 is shown to include a plurality ofheat recovery heat exchangers 226 (e.g., refrigeration circuits)configured to transfer heat from cold water loop 216 to hot water loop214. Heat recovery chiller subplant 204 is also shown to include severalpumps 228 and 230 configured to circulate the hot water and/or coldwater through heat recovery heat exchangers 226 and to control the flowrate of the water through individual heat recovery heat exchangers 226.Cooling tower subplant 208 is shown to include a plurality of coolingtowers 238 configured to remove heat from the condenser water incondenser water loop 218. Cooling tower subplant 208 is also shown toinclude several pumps 240 configured to circulate the condenser water incondenser water loop 218 and to control the flow rate of the condenserwater through individual cooling towers 238.

Hot TES subplant 210 is shown to include a hot TES tank 242 configuredto store the hot water for later use. Hot TES subplant 210 may alsoinclude one or more pumps or valves configured to control the flow rateof the hot water into or out of hot TES tank 242. Cold TES subplant 212is shown to include cold TES tanks 244 configured to store the coldwater for later use. Cold TES subplant 212 may also include one or morepumps or valves configured to control the flow rate of the cold waterinto or out of cold TES tanks 244.

In some embodiments, one or more of the pumps in central plant 200(e.g., pumps 222, 224, 228, 230, 234, 236, and/or 240) or pipelines incentral plant 200 include an isolation valve associated therewith.Isolation valves may be integrated with the pumps or positioned upstreamor downstream of the pumps to control the fluid flows in central plant200. In various embodiments, central plant 200 may include more, fewer,or different types of devices and/or subplants based on the particularconfiguration of central plant 200 and the types of loads served bycentral plant 200.

Referring now to FIG. 3, a block diagram illustrating a central plantsystem 300 is shown, according to an exemplary embodiment. System 300 isshown to include a central plant controller 302, a building automationsystem (BAS) 308, and a plurality of subplants 202-212. Subplants202-212 may be the same as previously described with reference to FIG.2. For example, subplants 202-212 are shown to include a heater subplant202, a heat recovery chiller subplant 204, a chiller subplant 206, a hotTES subplant 210, and a cold TES subplant 212.

Each of subplants 202-212 is shown to include equipment 340 that can becontrolled by central plant controller 302 and/or building automationsystem 308 to optimize the performance of central plant 200. Equipment340 can include any of a variety of HVAC equipment operable to controlan environmental condition in a building. For example, equipment 340 caninclude heating devices 220, chillers 232, heat recovery heat exchangers226, cooling towers 238, thermal energy storage devices 242-244, pumps,valves, other devices of subplants 202-212, or any other type of HVACequipment or central plant equipment. Individual devices of equipment340 can be turned on or off to adjust the thermal energy load served byeach of subplants 202-212. In some embodiments, individual devices ofequipment 340 can be operated at variable capacities (e.g., operating achiller at 10% capacity or 60% capacity) according to an operatingsetpoint received from central plant controller 302.

In some embodiments, one or more of subplants 202-212 includes asubplant level controller configured to control the equipment 340 of thecorresponding subplant. For example, central plant controller 302 maydetermine an on/off configuration and global operating setpoints forequipment 340. In response to the on/off configuration and receivedglobal operating setpoints, the subplant controllers may turn individualdevices of equipment 340 on or off, and implement specific operatingsetpoints (e.g., damper position, vane position, fan speed, pump speed,etc.) to reach or maintain the global operating setpoints.

In some embodiments, the subplant level controllers receive subplantload setpoints from central plant controller 302. Each subplant levelcontroller may use the subplant load setpoint for the correspondingsubplant to select one or more devices of the equipment 340 within thesubplant to activate or deactivate in order to meet the subplant loadsetpoint in an energy-efficient manner. In other embodiments, theequipment selection and staging decisions (i.e., deciding which devicesto turn on/off) are performed by a low level optimizer 332 withincentral plant controller 302.

BAS 308 may be configured to monitor conditions within a controlledbuilding or building zone. For example, BAS 308 may receive input fromvarious sensors (e.g., temperature sensors, humidity sensors, airflowsensors, voltage sensors, etc.) distributed throughout the building andmay report building conditions to central plant controller 302. Buildingconditions may include, for example, a temperature of the building or azone of the building, a power consumption (e.g., electric load) of thebuilding, a state of one or more actuators configured to affect acontrolled state within the building, or other types of informationrelating to the controlled building. BAS 308 may operate subplants202-212 to affect the monitored conditions within the building and/or toserve the thermal energy loads of the building.

BAS 308 may receive control signals from central plant controller 302specifying on/off states and/or setpoints for equipment 340. BAS 308 maycontrol equipment 340 (e.g., via actuators, power relays, etc.) inaccordance with the control signals provided by central plant controller302. For example, BAS 308 may operate equipment 340 using closed loopcontrol to achieve the setpoints specified by central plant controller302. BAS 308 may be combined with central plant controller 302 or may bepart of a separate building automation system. In some embodiments, BAS308 is a METASYS brand building automation system or VERASYS brandbuilding automation system, as sold by Johnson Controls, Inc. Severalexamples of building automation systems which can be used as BAS 308 aredescribed in detail in U.S. patent application Ser. No. 15/182,580 filedJun. 14, 2016, and U.S. patent application Ser. No. 15/179,894 filedJun. 10, 2016. The entire disclosures of both of these patentapplications are incorporated by reference herein.

Central plant controller 302 may monitor the status of the controlledbuilding using information received from BAS 308. Central plantcontroller 302 may be configured to predict the thermal energy loads(e.g., heating loads, cooling loads, etc.) of the building for pluralityof time steps in a prediction window (e.g., using weather forecasts froma weather service 324). Central plant controller 302 may generate on/offdecisions and/or setpoints for equipment 340 to minimize the cost ofenergy consumed by subplants 202-212 to serve the predicted heatingand/or cooling loads for the duration of the prediction window.According to an exemplary embodiment, central plant controller 302 isintegrated within a single computer (e.g., one server, one housing,etc.). In various other exemplary embodiments, central plant controller302 can be distributed across multiple servers or computers (e.g., thatcan exist in distributed locations). In another exemplary embodiment,central plant controller 302 is integrated with a smart building managerthat manages multiple building systems and/or combined with BAS 308.

Central plant controller 302 is shown to include a communicationsinterface 304 and a processing circuit 306. Communications interface 304may include wired or wireless interfaces (e.g., jacks, antennas,transmitters, receivers, transceivers, wire terminals, etc.) forconducting data communications with various systems, devices, ornetworks. For example, communications interface 304 may include anEthernet card and port for sending and receiving data via anEthernet-based communications network and/or a WiFi transceiver forcommunicating via a wireless communications network. Communicationsinterface 304 may be configured to communicate via local area networksor wide area networks (e.g., the Internet, a building WAN, etc.) and mayuse a variety of communications protocols (e.g., BACnet, IP, LON, etc.).

Communications interface 304 may be a network interface configured tofacilitate electronic data communications between central plantcontroller 302 and various external systems or devices (e.g., BAS 308,subplants 202-212, etc.). For example, central plant controller 302 mayreceive information from BAS 308 indicating one or more measured statesof the controlled building (e.g., temperature, humidity, electric loads,etc.) and one or more states of subplants 202-212 (e.g., equipmentstatus, power consumption, equipment availability, etc.). Communicationsinterface 304 may receive inputs from BAS 308 and/or subplants 202-212and may provide operating parameters (e.g., on/off decisions, setpoints,etc.) to subplants 202-212 via BAS 308. The operating parameters maycause subplants 202-212 to activate, deactivate, or adjust a setpointfor various devices of equipment 340.

Still referring to FIG. 3, processing circuit 306 is shown to include aprocessor 310 and memory 312. Processor 310 may be a general purpose orspecific purpose processor, an application specific integrated circuit(ASIC), one or more field programmable gate arrays (FPGAs), a group ofprocessing components, or other suitable processing components.Processor 310 may be configured to execute computer code or instructionsstored in memory 312 or received from other computer readable media(e.g., CDROM, network storage, a remote server, etc.).

Memory 312 may include one or more devices (e.g., memory units, memorydevices, storage devices, etc.) for storing data and/or computer codefor completing and/or facilitating the various processes described inthe present disclosure. Memory 312 may include random access memory(RAM), read-only memory (ROM), hard drive storage, temporary storage,non-volatile memory, flash memory, optical memory, or any other suitablememory for storing software objects and/or computer instructions. Memory312 may include database components, object code components, scriptcomponents, or any other type of information structure for supportingthe various activities and information structures described in thepresent disclosure. Memory 312 may be communicably connected toprocessor 310 via processing circuit 306 and may include computer codefor executing (e.g., by processor 310) one or more processes describedherein.

Still referring to FIG. 3, memory 312 is shown to include a buildingstatus monitor 334. Central plant controller 302 may receive dataregarding the overall building or building space to be heated or cooledwith central plant 200 via building status monitor 334. In an exemplaryembodiment, building status monitor 334 may include a graphical userinterface component configured to provide graphical user interfaces to auser for selecting building requirements (e.g., overall temperatureparameters, selecting schedules for the building, selecting differenttemperature levels for different building zones, etc.).

Central plant controller 302 may determine on/off configurations andoperating setpoints to satisfy the building requirements received frombuilding status monitor 334. In some embodiments, building statusmonitor 334 receives, collects, stores, and/or transmits cooling loadrequirements, building temperature setpoints, occupancy data, weatherdata, energy data, schedule data, and other building parameters. In someembodiments, building status monitor 334 stores data regarding energycosts, such as pricing information available from utilities 326 (energycharge, demand charge, etc.).

Still referring to FIG. 3, memory 312 is shown to include a load/ratepredictor 322. Load/rate predictor 322 may be configured to predict thethermal energy loads ({circumflex over (l)}_(k)) of the building orcampus for each time step k (e.g., k=1 . . . n) of an optimizationperiod. Load/rate predictor 322 is shown receiving weather forecastsfrom a weather service 324. In some embodiments, load/rate predictor 322predicts the thermal energy loads {circumflex over (l)}_(k) as afunction of the weather forecasts. In some embodiments, load/ratepredictor 322 uses feedback from BAS 308 to predict loads {circumflexover (l)}_(k). Feedback from BAS 308 may include various types ofsensory inputs (e.g., temperature, flow, humidity, enthalpy, etc.) orother data relating to the controlled building (e.g., inputs from a HVACsystem, a lighting control system, a security system, a water system,etc.).

In some embodiments, load/rate predictor 322 receives a measuredelectric load and/or previous measured load data from BAS 308 (e.g., viabuilding status monitor 334). Load/rate predictor 322 may predict loads{circumflex over (l)}_(k) as a function of a given weather forecast({circumflex over (ϕ)}_(w)), a day type (day), the time of day (t), andprevious measured load data (Y_(k-1)). Such a relationship is expressedin the following equation:

{circumflex over (l)} _(k) =f({circumflex over (ϕ)}_(w),day,t|Y _(k-1))

In some embodiments, load/rate predictor 322 uses a deterministic plusstochastic model trained from historical load data to predict loads{circumflex over (l)}_(k). Load/rate predictor 322 may use any of avariety of prediction methods to predict loads {circumflex over (l)}_(k)(e.g., linear regression for the deterministic portion and an AR modelfor the stochastic portion). Load/rate predictor 322 may predict one ormore different types of loads for the building or campus. For example,load/rate predictor 322 may predict a hot water load {circumflex over(l)}_(Hot,k) and a cold water load {circumflex over (l)}_(Cold,k) foreach time step k within the prediction window.

Load/rate predictor 322 is shown receiving utility rates from utilities326. Utility rates may indicate a cost or price per unit of a resource(e.g., electricity, natural gas, water, etc.) provided by utilities 326at each time step k in the prediction window. In some embodiments, theutility rates are time-variable rates. For example, the price ofelectricity may be higher at certain times of day or days of the week(e.g., during high demand periods) and lower at other times of day ordays of the week (e.g., during low demand periods). The utility ratesmay define various time periods and a cost per unit of a resource duringeach time period. Utility rates may be actual rates received fromutilities 326 or predicted utility rates estimated by load/ratepredictor 322.

In some embodiments, the utility rates include demand charges for one ormore resources provided by utilities 326. A demand charge may define aseparate cost imposed by utilities 326 based on the maximum usage of aparticular resource (e.g., maximum energy consumption) during a demandcharge period. The utility rates may define various demand chargeperiods and one or more demand charges associated with each demandcharge period. In some instances, demand charge periods may overlappartially or completely with each other and/or with the predictionwindow. Advantageously, central plant optimizer 328 may be configured toaccount for demand charges in the high level optimization processperformed by high level optimizer 330. Utilities 326 may be defined bytime-variable (e.g., hourly) prices, a maximum service level (e.g., amaximum rate of consumption allowed by the physical infrastructure or bycontract) and, in the case of electricity, a demand charge or a chargefor the peak rate of consumption within a certain period.

Load/rate predictor 322 may store the predicted loads {circumflex over(l)}_(k) and the utility rates in memory 312 and/or provide thepredicted loads {circumflex over (l)}_(k) and the utility rates tocentral plant optimizer 328. Central plant optimizer 328 may use thepredicted loads {circumflex over (l)}_(k) and the utility rates todetermine an optimal load distribution for subplants 202-212 and togenerate on/off decisions and setpoints for equipment 340.

Still referring to FIG. 3, memory 312 is shown to include an centralplant optimizer 328. Central plant optimizer 328 may perform a cascadedoptimization process to optimize the performance of central plant 200.For example, central plant optimizer 328 is shown to include a highlevel optimizer 330 and a low level optimizer 332. High level optimizer330 may control an outer (e.g., subplant level) loop of the cascadedoptimization. High level optimizer 330 may determine an optimaldistribution of thermal energy loads across subplants 202-212 for eachtime step in the prediction window in order to optimize (e.g., minimize)the cost of energy consumed by subplants 202-212. Low level optimizer332 may control an inner (e.g., equipment level) loop of the cascadedoptimization. Low level optimizer 332 may determine how to best run eachsubplant at the load setpoint determined by high level optimizer 330.For example, low level optimizer 332 may determine on/off states and/oroperating setpoints for various devices of equipment 340 in order tooptimize (e.g., minimize) the energy consumption of each subplant whilemeeting the thermal energy load setpoint for the subplant. The cascadedoptimization process is described in greater detail with reference toFIG. 4.

Still referring to FIG. 3, memory 312 is shown to include a subplantmonitor 338. Subplant monitor 338 may store historical data regardingpast operating statuses, past operating setpoints, and instructions forcalculating and/or implementing control parameters for subplants202-212. Subplant monitor 338 may also receive, store, and/or transmitdata regarding the conditions of individual devices of equipment 340,such as operating efficiency, equipment degradation, a date since lastservice, a lifespan parameter, a condition grade, or otherdevice-specific data. Subplant monitor 338 may receive data fromsubplants 202-212 and/or BAS 308 via communications interface 304.Subplant monitor 338 may also receive and store on/off statuses andoperating setpoints from low level optimizer 332.

Data and processing results from central plant optimizer 328, subplantmonitor 338, or other modules of central plant controller 302 may beaccessed by (or pushed to) monitoring and reporting applications 336.Monitoring and reporting applications 336 may be configured to generatereal time system health dashboards that can be viewed and navigated by auser (e.g., a central plant engineer). For example, monitoring andreporting applications 336 may include a web-based monitoringapplication with several graphical user interface (GUI) elements (e.g.,widgets, dashboard controls, windows, etc.) for displaying keyperformance indicators (KPI) or other information to users of a GUI. Inaddition, the GUI elements may summarize relative energy use andintensity across central plants in different buildings (real ormodeled), different campuses, or the like. Other GUI elements or reportsmay be generated and shown based on available data that allow users toassess performance across one or more central plants from one screen.The user interface or report (or underlying data engine) may beconfigured to aggregate and categorize operating conditions by building,building type, equipment type, and the like. The GUI elements mayinclude charts or histograms that allow the user to visually analyze theoperating parameters and power consumption for the devices of thecentral plant.

Still referring to FIG. 3, central plant controller 302 may include oneor more GUI servers, web services 314, or GUI engines 316 to supportmonitoring and reporting applications 336. In various embodiments,applications 336, web services 314, and GUI engine 316 may be providedas separate components outside of central plant controller 302 (e.g., aspart of a smart building manager). Central plant controller 302 may beconfigured to maintain detailed historical databases (e.g., relationaldatabases, XML, databases, etc.) of relevant data and includes computercode modules that continuously, frequently, or infrequently query,aggregate, transform, search, or otherwise process the data maintainedin the detailed databases. Central plant controller 302 may beconfigured to provide the results of any such processing to otherdatabases, tables, XML files, or other data structures for furtherquerying, calculation, or access by, for example, external monitoringand reporting applications.

Central plant controller 302 is shown to include configuration tools318. Configuration tools 318 can allow a user to define (e.g., viagraphical user interfaces, via prompt-driven wizards, etc.) how centralplant controller 302 should react to changing conditions in the centralplant subsystems. In an exemplary embodiment, configuration tools 318allow a user to build and store condition-response scenarios that cancross multiple central plant devices, multiple building systems, andmultiple enterprise control applications (e.g., work order managementsystem applications, entity resource planning applications, etc.). Forexample, configuration tools 318 can provide the user with the abilityto combine data (e.g., from subsystems, from event histories) using avariety of conditional logic. In varying exemplary embodiments, theconditional logic can range from simple logical operators betweenconditions (e.g., AND, OR, XOR, etc.) to pseudo-code constructs orcomplex programming language functions (allowing for more complexinteractions, conditional statements, loops, etc.). Configuration tools318 can present user interfaces for building such conditional logic. Theuser interfaces may allow users to define policies and responsesgraphically. In some embodiments, the user interfaces may allow a userto select a pre-stored or pre-constructed policy and adapt it or enableit for use with their system.

Referring now to FIG. 4, a block diagram illustrating a portion ofcentral plant system 300 in greater detail is shown, according to anexemplary embodiment. FIG. 4 illustrates the cascaded optimizationprocess performed by central plant optimizer 328 to optimize theperformance of central plant 200. In the cascaded optimization process,high level optimizer 330 performs a subplant level optimization thatdetermines an optimal distribution of thermal energy loads acrosssubplants 202-212 for each time step in the prediction window in orderto minimize the cost of energy consumed by subplants 202-212. Low leveloptimizer 332 performs an equipment level optimization that determineshow to best run each subplant at the subplant load setpoint determinedby high level optimizer 330. For example, low level optimizer 332 maydetermine on/off states and/or operating setpoints for various devicesof equipment 340 in order to optimize the energy consumption of eachsubplant while meeting the thermal energy load setpoint for thesubplant.

One advantage of the cascaded optimization process performed by centralplant optimizer 328 is the optimal use of computational time. Forexample, the subplant level optimization performed by high leveloptimizer 330 may use a relatively long time horizon due to theoperation of the thermal energy storage. However, the equipment leveloptimization performed by low level optimizer 332 may use a much shortertime horizon or no time horizon at all since the low level systemdynamics are relatively fast (compared to the dynamics of the thermalenergy storage) and the low level control of equipment 340 may behandled by BAS 308. Such an optimal use of computational time makes itpossible for central plant optimizer 328 to perform the central plantoptimization in a short amount of time, allowing for real-timepredictive control. For example, the short computational time enablescentral plant optimizer 328 to be implemented in a real-time planningtool with interactive feedback.

Another advantage of the cascaded optimization performed by centralplant optimizer 328 is that the central plant optimization problem canbe split into two cascaded subproblems. The cascaded configurationprovides a layer of abstraction that allows high level optimizer 330 todistribute the thermal energy loads across subplants 202-212 withoutrequiring high level optimizer 330 to know or use any details regardingthe particular equipment configuration within each subplant. Theinterconnections between equipment 340 within each subplant may behidden from high level optimizer 330 and handled by low level optimizer332. For purposes of the subplant level optimization performed by highlevel optimizer 330, each subplant may be completely defined by one ormore subplant curves 342.

Low level optimizer 332 may generate and provide subplant curves 342 tohigh level optimizer 330. Subplant curves 342 may indicate the rate ofutility use by each of subplants 202-212 (e.g., electricity use measuredin kW, water use measured in L/s, etc.) as a function of the subplantload. In some embodiments, low level optimizer 332 generates subplantcurves 342 based on equipment models 320 (e.g., by combining equipmentmodels 320 for individual devices into an aggregate curve for thesubplant). Low level optimizer 332 may generate subplant curves 342 byrunning the low level optimization process for several different loadsand weather conditions to generate multiple data points. Low leveloptimizer 332 may fit a curve to the data points to generate subplantcurves 342. In other embodiments, low level optimizer 332 provides thedata points to high level optimizer 330 and high level optimizer 330generates the subplant curves using the data points.

High level optimizer 330 may receive the load and rate predictions fromload/rate predictor 322 and the subplant curves 342 from low leveloptimizer 332. The load predictions may be based on weather forecastsfrom weather service 324 and/or information from building automationsystem 308 (e.g., a current electric load of the building, measurementsfrom the building, a history of previous loads, a setpoint trajectory,etc.). The utility rate predictions may be based on utility ratesreceived from utilities 326 and/or utility prices from another datasource. High level optimizer 330 may determine the optimal loaddistribution for subplants 202-212 (e.g., a subplant load for eachsubplant) for each time step the prediction window and may provide thesubplant loads as setpoints to low level optimizer 332. In someembodiments, high level optimizer 330 determines the subplant loads byminimizing the total operating cost of central plant 200 over theprediction window. In other words, given a predicted load and utilityrate information from load/rate predictor 322, high level optimizer 330may distribute the predicted load across subplants 202-212 over theoptimization period to minimize operating cost.

In some instances, the optimal load distribution may include using TESsubplants 210 and/or 212 to store thermal energy during a first timestep for use during a later time step. Thermal energy storage mayadvantageously allow thermal energy to be produced and stored during afirst time period when energy prices are relatively low and subsequentlyretrieved and used during a second time period when energy proves arerelatively high. The high level optimization may be different from thelow level optimization in that the high level optimization has a longertime constant due to the thermal energy storage provided by TESsubplants 210-212. The high level optimization may be described by thefollowing equation:

$\theta_{HL}^{*} = {\arg \mspace{11mu} {\min\limits_{\theta_{HL}}{J_{HL}\left( \theta_{HL} \right)}}}$

where θ*_(HL) contains the optimal high level decisions (e.g., theoptimal load for each of subplants 202-212) for the entire optimizationperiod and J_(HL) is the high level cost function.

To find the optimal high level decisions θ*_(HL), high level optimizer330 may minimize the high level cost function J_(HL). The high levelcost function J_(HL) may be the sum of the economic (e.g., monetary)costs of each utility consumed by each of subplants 202-212 for theduration of the optimization period. In some embodiments, the high levelcost function J_(HL) may be described using the following equation:

${J_{HL}\left( \theta_{HL} \right)} = {\sum\limits_{k = 1}^{n_{h}}\; {\sum\limits_{i = 1}^{n_{s}}\; \left\lbrack {\sum\limits_{j = 1}^{n_{u}}\; {{t_{s} \cdot c_{jk}}{u_{jik}\left( \theta_{HL} \right)}}} \right\rbrack}}$

where n_(h) is the number of time steps k in the optimization period,n_(s) is the number of subplants, t_(s) is the duration of a time step,c_(jk) is the economic cost of utility j at a time step k of theoptimization period, and u_(jik) is the rate of use of utility j bysubplant i at time step k.

In some embodiments, the cost function J_(HL) includes an additionaldemand charge term such as:

$w_{d}c_{demand}{\max\limits_{n_{h}}\left( {{u_{elec}\left( \theta_{HL} \right)},u_{\max,{ele}}} \right)}$

where w_(d) is a weighting term, c_(demand) is the demand cost, and themax( ) term selects the peak electricity use during the applicabledemand charge period. Accordingly, the high level cost function J_(HL)may be described by the equation:

${J_{HL}\left( \theta_{HL} \right)} = {{\sum\limits_{k = 1}^{n_{h}}\; {\sum\limits_{i = 1}^{n_{s}}\; \left\lbrack {\sum\limits_{j = 1}^{n_{u}}\; {{t_{s} \cdot c_{jk}}{u_{jik}\left( \theta_{HL} \right)}}} \right\rbrack}} + {w_{d}c_{demand}{\max\limits_{n_{h}}\left( {{u_{elec}\left( \theta_{HL} \right)},u_{\max,{ele}}} \right)}}}$

The decision vector θ_(HL) may be subject to several constraints. Forexample, the constraints may require that the subplants not operate atmore than their total capacity, that the thermal storage not charge ordischarge too quickly or under/over flow for the tank, and that thethermal energy loads for the building or campus are met. Theserestrictions may lead to both equality and inequality constraints on thehigh level optimization problem.

In some embodiments, the high level optimization performed by high leveloptimizer 330 is the same or similar to the high level optimizationprocess described in U.S. patent application Ser. No. 14/634,609 filedFeb. 27, 2015 and titled “High Level Central Plant Optimization,” theentire disclosure of which is incorporated by reference herein. Highlevel optimizer 330 may include some or all of the features and/orfunctionality of the high level optimization module described in U.S.patent application Ser. No. 14/634,609.

Still referring to FIG. 4, low level optimizer 332 may use the subplantloads determined by high level optimizer 330 to determine optimal lowlevel decisions θ*_(LL) (e.g. binary on/off decisions, flow setpoints,temperature setpoints, etc.) for equipment 340. The low leveloptimization process may be performed for each of subplants 202-212. Invarious embodiments, the low level optimization process may be performedby centralized low level optimizer 332 that performs a separate lowlevel optimization for each of subplants 202-212 or by a set of subplantlevel controllers that operate within each subplant (e.g., each subplantcontroller running an instance of low level optimizer 332). Low leveloptimizer 332 may be responsible for determining which devices of thesubplant to use and/or the operating setpoints for such devices thatwill achieve the subplant load setpoint while minimizing energyconsumption. The low level optimization may be described using thefollowing equation:

$\theta_{LL}^{*} = {\arg \mspace{11mu} {\min\limits_{\theta_{LL}}{J_{LL}\left( \theta_{LL} \right)}}}$

where θ*_(LL) contains the optimal low level decisions and J_(LL) is thelow level cost function.

To find the optimal low level decisions θ*_(LL), low level optimizer 332may minimize the low level cost function J_(LL). The low level costfunction J_(LL) may represent the total energy consumption for all ofequipment 340 in the applicable subplant. The low level cost functionJ_(LL) may be described using the following equation:

${J_{LL}\left( \theta_{LL} \right)} = {\sum\limits_{j = 1}^{N}\; {t_{s} \cdot b_{j} \cdot {u_{j}\left( \theta_{LL} \right)}}}$

where N is the number of devices of equipment 340 in the subplant, t_(s)is the duration of a time step, b_(j) is a binary on/off decision (e.g.,0=off, 1=on), and u_(j) is the energy used by device j as a function ofthe setpoint θ_(LL). Each device may have continuous variables which canbe changed to determine the lowest possible energy consumption for theoverall input conditions.

Low level optimizer 332 may minimize the low level cost function J_(LL)subject to inequality constraints based on the capacities of equipment340 and equality constraints based on energy, momentum, and/or massbalances. In some embodiments, the optimal low level decisions θ*_(LL)are constrained by switching constraints defining a short horizon formaintaining a device in an on or off state after a binary on/off switch.The switching constraints may prevent devices from being rapidly cycledon and off. In some embodiments, low level optimizer 332 performs theequipment level optimization without considering system dynamics. Theoptimization process may be slow enough to safely assume that theequipment control has reached its steady-state. Thus, low leveloptimizer 332 may determine the optimal low level decisions θ*_(LL) atan instance of time rather than over a long horizon.

Low level optimizer 332 may determine optimum operating statuses (e.g.,on or off) for a plurality of devices of equipment 340. According to anexemplary embodiment, the on/off combinations may be determined usingbinary optimization and quadratic compensation. Binary optimization mayminimize a cost function representing the power consumption of devicesin the applicable subplant. In some embodiments, non-exhaustive (i.e.,not all potential combinations of devices are considered) binaryoptimization is used. Quadratic compensation may be used in consideringdevices whose power consumption is quadratic (and not linear). Low leveloptimizer 332 may also determine optimum operating setpoints forequipment using nonlinear optimization. Nonlinear optimization mayidentify operating setpoints that further minimize the low level costfunction J_(LL). Low level optimizer 332 may provide the on/offdecisions and setpoints to building automation system 308 for use incontrolling the HVAC equipment 340.

In some embodiments, the low level optimization performed by low leveloptimizer 332 is the same or similar to the low level optimizationprocess described in U.S. patent application Ser. No. 14/634,615 filedFeb. 27, 2015 and titled “Low Level Central Plant Optimization,” theentire disclosure of which is incorporated by reference herein. Lowlevel optimizer 332 may include some or all of the features and/orfunctionality of the low level optimization module described in U.S.patent application Ser. No. 14/634,615.

Still referring to FIG. 4, central plant system 300 is shown to includea predictive modeling system 402. Predictive modeling system 402 isshown receiving monitored variables and operating points from BAS 308.The monitored variables can include, for example, measured variables(e.g., measured temperature, measured air flow rate, etc.), calculatedvariables (e.g., heat capacity of a substance at a given temperature,enthalpy, coefficient of performance, etc.), control variables (e.g.,setpoints, equipment operating points, on/off decisions, etc.),equipment parameters (e.g., rated load, control parameters, etc.), orany other variables that characterize the operation of various devicesof HVAC equipment 340. Monitored variables can be received from BAS 308,controller 302, or directly from HVAC equipment 340. For example,monitored variables can include sensor measurements received fromvarious sensors of HVAC equipment 340. The operating points can includesetpoints (e.g., load setpoints, capacity setpoints, etc.), operatingstates, or other variables that indicate the current operating state ofHVAC equipment 340. The operating points can be received from BAS 308(as shown in FIG. 4), from low level optimizer 332, or from high leveloptimizer 330. For example, the operating points can include equipmentsetpoints generated by low level optimizer 332, load setpoints generatedby high level optimizer 330, or other types of operating points.

Predictive modeling system 402 can be configured to generate and provideequipment models 320 and combined model predictions 346 to low leveloptimizer 332. Equipment models 320 can include any of a variety ofmodels that characterize the performance of HVAC equipment 340. In someembodiments, each of equipment models 320 corresponds to an individualHVAC device of HVAC equipment 340 (e.g., an individual chiller, anindividual boiler, an individual compressor, etc.) and can be used topredict the performance of the corresponding HVAC device. For example,equipment models 320 can include power consumption models that can beused to predict the power consumption of individual HVAC devices of HVACequipment 340 at various operating points. In some embodiments,equipment models 320 can be used to predict various output variables(e.g., coefficient of performance, power consumption, etc.) of HVACequipment 340 as a function of the monitored variables and/or operatingpoints.

In some embodiments, equipment models 320 define power consumption as afunction of equipment load and/or equipment setpoints. For example, anequipment model 320 for a chiller may define the power consumption ofthe chiller as a function of cold water production and/or chiller loadsetpoints. In general, an equipment model 320 for a particular HVACdevice may define the relationship between the inputs to the HVAC deviceand the outputs of the HVAC device. Equipment models 320 can be used topredict an amount of input resources (e.g., electricity, water, naturalgas, etc.) required to produce a desired amount of an output resource(e.g., chilled water, hot water, electricity, etc.). Equipment models320 can be used by low level optimizer 332 to predict the powerconsumption of various devices of HVAC equipment 340 that will resultfrom the on/off decisions and setpoints selected by low level optimizer332.

As described above, low level optimizer 332 can use equipment models 320to generate subplant curves 342 which aggregate the equipment models fora set of HVAC equipment 340 in a single subplant. Central plantoptimizer 328 can use subplant curves 342 and/or equipment models 320 tooptimize equipment operation. In some embodiments, central plantoptimizer 328 operates as a planning tool. For example, central plantoptimizer 328 can operate a simulated plant under various hypotheticalscenarios to evaluate system performance under different sets ofconditions. The simulated plant can be adjusted to reflect plannedequipment purchases, installation of energy-efficient equipment, orother planned changes to allow central plant optimizer 328 to runvarious hypothetical scenarios before the changes are actually made tothe physical plant. In other embodiments, central plant optimizer 328operates as a real-time operational tool to optimize the current runningconditions of a physical plant, as previously described.

In some embodiments, equipment models 320 include multiple predictivemodels for each device of HVAC equipment 340. Each of the predictivemodels for a given HVAC device may predict the same variable using adifferent prediction technique. For example, a first equipment model 320for a chiller may predict the coefficient of performance (COP) of thechiller using a bi-quadratic model, whereas a second equipment model 320for the chiller may predict the COP of the chiller using a multivariatepolynomial model, and a third equipment model 320 for the chiller maypredict the COP of the chiller using a liner regression model. Theoutput or prediction of a single equipment model 320 is referred toherein as a component model prediction. Throughout this disclosure, theterms “equipment model” and “component model” are used interchangeably.Each of the equipment models 320 can use the same set of input variablesor a different set of input variables to generate the component modelpredictions.

In some embodiments, predictive modeling system 402 uses multipleequipment models 320 for the same predicted variable to generate eachcombined model prediction 346. For example, predictive modeling system402 can generate multiple different component model predictions for eachpredicted variable using multiple different equipment models 320.Predictive modeling system 402 can then combine the component modelpredictions for a given predicted variable to form a combined modelprediction 346. Predictive modeling system 402 can use any of a varietyof techniques to combine the component model predictions. For example,predictive modeling system 402 can use equal weighting, principalcomponents, trimmed means, constrained or unconstrained regression,artificial neural networks, variance weighting, ensemble machinelearning techniques (e.g., boosting, bagging, etc.), or any othercombination technique to generate a combined model prediction 346 frommultiple component model predictions. Several of these combinationtechniques are described in greater detail below.

Combining multiple component model predictions to form a combined modelprediction 346 has several advantages. For example, different componentmodels may use different input variables to predict the same outputvariable. This results in diversity of model inputs when the componentmodel predictions are combined, which can increase the accuracy of thecombined model prediction. Additionally, a diversity of component modeltypes can improve the accuracy of the combined model prediction incircumstances when specific types of component models may lack accuracy.For example, some component model types may be more accurate than othersat predicting chiller power consumption under high load conditions, butless accurate than the others at predicting chiller power consumptionunder low load conditions. The existence of multiple different componentmodel types increases the probability that not all of the componentmodels will lack accuracy under the same set of conditions. Furthermore,using multiple different component models to predict the same variableallows for outlier predictions to be identified and removed from the setof predictions before combination. This can also increase the accuracyof the combined model prediction 346 by pruning outlier predictions.

Predictive Modeling System

Referring now to FIG. 5, a block diagram illustrating predictivemodeling system 402 in greater detail is shown, according to anexemplary embodiment. Predictive modeling system 402 is shown to includea communications interface 502 and a processing circuit 504.Communications interface 502 may include wired or wireless interfaces(e.g., jacks, antennas, transmitters, receivers, transceivers, wireterminals, etc.) for conducting data communications with varioussystems, devices, or networks. For example, communications interface 502may include an Ethernet card and port for sending and receiving data viaan Ethernet-based communications network and/or a WiFi transceiver forcommunicating via a wireless communications network. Communicationsinterface 502 may be configured to communicate via local area networksor wide area networks (e.g., the Internet, a building WAN, etc.) and mayuse a variety of communications protocols (e.g., BACnet, IP, LON, etc.).

Communications interface 502 may be a network interface configured tofacilitate electronic data communications between predictive modelingsystem 402 and various external systems or devices (e.g., BAS 308,central plant controller 302, HVAC equipment 340, etc.). For example,predictive modeling system 402 may receive samples of monitoredvariables and operating points from BAS 308. The monitored variables caninclude measured variables (e.g., measured temperature, measured airflow rate, etc.), calculated variables (e.g., heat capacity of asubstance at a given temperature, enthalpy, coefficient of performance,etc.), control variables (e.g., setpoints, equipment operating points,on/off decisions, etc.), equipment parameters (e.g., rated load, controlparameters, etc.), or any other variables that characterize theoperation of various devices of HVAC equipment 340. The operating pointscan include setpoints (e.g., load setpoints, capacity setpoints, etc.),operating states, or other variables that indicate the current operatingstate of HVAC equipment 340. Predictive modeling system 402 can use themonitored variables and operating points to generate a combined modelprediction, which can be provided to central plant controller 302 viacommunications interface 502.

Processing circuit 504 is shown to include a processor 506 and memory508. Processor 506 may be a general purpose or specific purposeprocessor, an application specific integrated circuit (ASIC), one ormore field programmable gate arrays (FPGAs), a group of processingcomponents, or other suitable processing components. Processor 506 maybe configured to execute computer code or instructions stored in memory508 or received from other computer readable media (e.g., CDROM, networkstorage, a remote server, etc.).

Memory 508 may include one or more devices (e.g., memory units, memorydevices, storage devices, etc.) for storing data and/or computer codefor completing and/or facilitating the various processes described inthe present disclosure. Memory 508 may include random access memory(RAM), read-only memory (ROM), hard drive storage, temporary storage,non-volatile memory, flash memory, optical memory, or any other suitablememory for storing software objects and/or computer instructions. Memory508 may include database components, object code components, scriptcomponents, or any other type of information structure for supportingthe various activities and information structures described in thepresent disclosure. Memory 508 may be communicably connected toprocessor 506 via processing circuit 504 and may include computer codefor executing (e.g., by processor 506) one or more processes describedherein.

HVAC Component Models

Still referring to FIG. 5, predictive modeling system 402 is shown toinclude several HVAC component models 510. HVAC component models 510 caninclude any of a variety of predictive models configured to predict theperformance of a HVAC component based on a set of input variables (e.g.,monitored variables and/or operating points). In some embodiments, eachof HVAC component models 510 corresponds to a particular HVAC device, aparticular type of HVAC device (e.g., a chiller, a boiler, an actuator,etc.) or a particular model of HVAC device (e.g., chiller model A,chiller model B, etc.) and can be used to predict the performance of thecorresponding HVAC device, device type, or model. For example, HVACcomponent models 510 can include power consumption models that can beused to predict the power consumption of various HVAC devices. In someembodiments, HVAC component models 510 define power consumption as afunction of equipment load and/or equipment setpoints. For example, theHVAC component model for a chiller may define the power consumption ofthe chiller as a function of cold water production and/or chiller loadsetpoints.

In some embodiments, HVAC component models 510 define the relationshipbetween the inputs to a HVAC device and the outputs of the HVAC device.HVAC component models 510 can be used to predict an amount of inputresources (e.g., electricity, water, natural gas, etc.) required toproduce a desired amount of an output resource (e.g., chilled water, hotwater, electricity, etc.). HVAC component models 510 can be used by lowlevel optimizer 332 to predict the power consumption of various devicesof HVAC equipment 340 that will result from the on/off decisions andsetpoints selected by low level optimizer 332.

In some embodiments, HVAC component models 510 are configured to predictperformance-related variables (e.g., coefficient of performance, powerconsumption, etc.) of HVAC equipment 340 as a function of the monitoredvariables and/or operating points. In some embodiments, HVAC componentmodels 510 define the coefficient of performance of a HVAC device as afunction of various input variables. For example, the HVAC componentmodel for a chiller may define the chiller's coefficient of performanceCOP as a function of the water temperature entering the chiller'scondenser T_(ci), the water temperature entering the chiller'sevaporator T_(ei), the water temperature leaving the chiller'sevaporator T_(eo), the evaporator (chiller) load Q_(e), the chillerrated load Q_(r), the mass flow rate of condenser (cooling) water {dotover (m)}_(c), the mass flow rate of evaporator (chilled) water {dotover (m)}_(e), the heat capacity of water at condenser temperaturecp_(c), the heat capacity of water at evaporator temperature cp_(e),and/or other variables that can be provided as inputs to HVAC componentmodels 510. An example chiller and a set of variables which can beincluded in HVAC component models 510 for the chiller are described ingreater detail with reference to FIG. 6.

In some embodiments, HVAC component models 510 include multiplepredictive models for each HVAC device of HVAC equipment 340. Each ofHVAC component models 510 may predict the same variable using adifferent prediction technique. For example, HVAC component models 510are shown to include Gordon-Ng models 512, bi-quadratic models 514,multivariate models 516, and other models 518. Gordon-Ng models 512 canbe configured to predict the value of a performance variable (e.g.,coefficient of performance, power consumption, etc.) using a Gordon-Ngprediction technique. Similarly, bi-quadratic models 514 can beconfigured to predict the value of the same performance variable using abi-quadratic prediction technique, and multivariate models 516 can beconfigured to predict the value of the same performance variable using amultivariate prediction technique. These and several other predictiontechniques which can be used by HVAC component models 510 are describedin greater detail below.

Each of HVAC component models 510 can be configured to predict the sameperformance variable. For example, each of the HVAC component models 510for a chiller can independently predict the coefficient of performanceof the chiller, resulting in multiple independent predictions. DifferentHVAC component models 510 can use the same set of input variables ordifferent sets of input variables to perform their predictions. Each ofthe predictions generated by HVAC component models 510 (i.e., thecomponent model predictions) can be provided as an output to predictioncombiners 520.

Several examples of HVAC component models 510 are described in thefollowing paragraphs. Although HVAC component models 510 are describedprimarily with reference to a chiller and include chiller-relatedvariables, it should be understood that HVAC component models 510 canmodel the performance of any type of HVAC equipment or buildingequipment. For example, HVAC component models 510 can model theperformance of chillers, air handling units, actuators, pumps, valves,boilers, thermal energy storage, electrical energy storage (e.g.,batteries), or other types of HVAC equipment or HVAC equipment 340. HVACcomponent models 510 for different types of equipment can includedifferent variables (e.g., different predictor variables, differentperformance variables, etc.) in addition to or in place of thechiller-specific variables included in the models below.

HVAC component models 510 are shown to include Gordon-Ng models 512. Insome embodiments, Gordon-Ng models 512 include a Gordon-Ng universalmodel with entering evaporator temperature (GN-U T_(ei)). This model isderived from thermodynamic and heat transfer principles in the chiller,and it has three independent variables and three parameters. The GN-UT_(ei) model has a functional form of:

${{\frac{T_{ei}}{T_{ci}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} - 1} = {{\beta_{1}\left( \frac{T_{ei}}{Q_{e}} \right)} + {\beta_{2}\left( \frac{T_{ci} - T_{ei}}{T_{ci}Q_{e}} \right)} + {\beta_{3}\left( {\frac{Q_{e}}{T_{ci}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} \right)}}$

where T_(ei) is the temperature of the water entering the evaporator,T_(ci) is the temperature of the water entering the condenser, (2, isthe evaporator (chiller) load, and COP is the coefficient of performanceof the chiller. The parameters β₁, β₂, and β₃ are regression modelparameters and can be identified by fitting the model to a set oftraining data. In some embodiments, the GN-U T_(ei) model is aregression model with no constant term and three parameters. It has theadvantage of being based on physical quantities and first principles.

In some embodiments, Gordon-Ng models 512 include a Gordon-Ng universalmodel with leaving evaporator temperature (GN-U T_(eo)). This model is amodification of the Gordon-Ng universal model GN-U T_(ei) where thetemperature of the water leaving the evaporator T_(eo) is used in placeof the temperature of the water entering the evaporator T_(ei). The GN-UT_(eo) model has a functional form of:

${{\frac{T_{eo}}{T_{ci}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} - 1} = {{\beta_{1}\left( \frac{T_{eo}}{Q_{e}} \right)} + {\beta_{2}\left( \frac{T_{ci} - T_{eo}}{T_{ci}Q_{e}} \right)} + {\beta_{3}\left( {\frac{Q_{e}}{T_{ci}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} \right)}}$

where T_(eo) is the temperature of the water leaving the evaporator,T_(ci) is the temperature of the water entering the condenser, Q_(e) isthe evaporator (chiller) load, and COP is the coefficient of performanceof the chiller. The parameters β₁, β₂, and β₃ are regression modelparameters and can be identified by fitting the model to a set oftraining data. In some embodiments, the GN-U T_(eo) model is aregression model with no constant term, three independent variables, andthree parameters. It has the advantage of being based on physicalquantities and first principles.

In some embodiments, Gordon-Ng models 512 include a Gordon-Ng model withleaving evaporator temperature and condenser/evaporator flows (GN-KN).This model was developed as at Johnson Controls Inc. as a modificationto the Gordon-Ng universal chiller model GN-U T_(ei). The modificationsto the original model include water mass flow in the condenser {dot over(m)}_(c) and the evaporator {dot over (m)}_(e) as well as a substitutionof the water temperature leaving the evaporator T_(eo) for the watertemperature entering the evaporator T_(ei). The GN-KN model has afunctional form of:

${{\frac{T_{eo}}{T_{ci}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} - 1} = {{\beta_{1}\left( \frac{T_{eo}}{Q_{e}} \right)} + {\beta_{2}\left( \frac{T_{ci} - T_{eo}}{T_{ci}Q_{e}} \right)} + {\beta_{3}\left( {\frac{Q_{e}}{T_{ci}{\overset{.}{m}}_{e}{cp}_{c}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} \right)} + {\beta_{4}\left( {\frac{Q_{e}}{T_{ci}{\overset{.}{m}}_{e}{cp}_{e}}\left\lbrack {1 + \frac{1}{COP}} \right\rbrack} \right)}}$

where T_(eo) is the temperature of the water leaving the evaporator,T_(ci) is the temperature of the water entering the condenser, Q_(e), isthe evaporator (chiller) load, {dot over (m)}_(c) is the mass flow rateof the cooling water in the condenser, {dot over (m)}_(e) is the massflow rate of the chilled water in the evaporator, cp_(c) is the heatcapacity of water at the temperature of the condenser, cp_(e) is theheat capacity of water at the temperature of the evaporator, and COP isthe coefficient of performance of the chiller. The parameters β₁, β₂, β₃and β₄ are regression model parameters and can be identified by fittingthe model to a set of training data. In some embodiments, the GN-KNmodel is a regression model with no constant term and four parameters.It has the advantage of being based on physical quantities and firstprinciples.

In some embodiments, Gordon-Ng models 512 include a Gordon-Ng simplifiedmodel (GN-S). This version of the Gordon-Ng universal model GN-U T_(ei)simplifies the left side of the equation to isolate the COP. The GN-Smodel has a functional form of:

$\frac{1}{COP} = {{- 1} + \frac{T_{ci}}{T_{eo}} + {\frac{1}{Q_{e}}\left\lbrack {{- \beta_{1}} + {\beta_{2}T_{ci}} - {\beta_{3}\frac{T_{ci}}{T_{eo}}}} \right\rbrack}}$

where T_(eo) is the temperature of the water leaving the evaporator,T_(ci) is the temperature of the water entering the condenser, Q_(e) isthe evaporator (chiller) load, and COP is the coefficient of performanceof the chiller. The parameters β₁, β₂, and β₃ are regression modelparameters and can be identified by fitting the model to a set oftraining data. The GN-S model has the advantage of being based onphysical quantities and first principles.

Still referring to FIG. 5, HVAC component models 510 are shown toinclude bi-quadratic models 514. In some embodiments, bi-quadraticmodels 514 include a simple bi-quadratic model (BQ) which uses only twoindependent variables, the evaporator (chiller) load Q_(e) and thetemperature of the water entering the condenser T_(ci). The BQ model hasa functional form of:

$\frac{1}{COP} = {\beta_{1} + {\beta_{2}\left( \frac{1}{Q_{e}} \right)} + {\beta_{3}Q_{e}} + {\beta_{4}\left( \frac{T_{ci}}{Q_{e}} \right)} + {\beta_{5}\left( \frac{T_{ci}^{2}}{Q_{e}} \right)} + {\beta_{6}T_{ci}} + {\beta_{7}Q_{e}T_{ci}} + {\beta_{8}T_{ci}^{2}} + {\beta_{9}Q_{e}T_{ci}^{2}}}$

where T_(ci) is the temperature of the water entering the condenser,Q_(e) is the evaporator (chiller) load, and COP is the coefficient ofperformance of the chiller. The parameters β₁-β₉ are regression modelparameters and can be identified by fitting the model to a set oftraining data.

In some embodiments, bi-quadratic models 514 include a bi-quadraticmodel (BQ-D) which uses two independent variables, lift and part loadratio. The form of the BQ-D model has been altered from the original BQmodel by pulling out some constants that can be grouped into theparameters. The BQ-D model has a functional form of:

$\frac{1}{COP} = {\beta_{1} + {\beta_{2}\left( \frac{Q_{e}}{Q_{r}} \right)} + {\beta_{3}\left( \frac{Q_{e}}{Q_{r}} \right)}^{2} + {\beta_{4}\left( {T_{ci} - T_{eo}} \right)} + {\beta_{5}\left( {T_{ci} - T_{eo}} \right)}^{2} + {\beta_{6}\left( {\left( {T_{ci} - T_{eo}} \right)\left( \frac{Q_{e}}{Q_{r}} \right)} \right)}}$

where the ratio of chiller load Q_(e) to chiller rated load Q_(r) is thepart load ratio (i.e., PLR=Q_(e)/Q_(r)) and the difference between thetemperature of the water entering the condenser T_(ci) and thetemperature of the water leaving the evaporator T_(eo) is the lift(i.e., Lift=T_(ci)−T_(eo)). The parameters β₁-β₆ are regression modelparameters and can be identified by fitting the model to a set oftraining data.

In some embodiments, bi-quadratic models 514 include a bi-quadraticmodel (BQ-V) which incorporates an additional Lift*PLR² term in themodel's functional form. The BQ-V model has two independent variables,seven parameters, and a functional form of:

$\frac{1}{COP} = {\beta_{1} + {\beta_{2}\left( \frac{Q_{e}}{Q_{r}} \right)} + {\beta_{3}\left( \frac{Q_{e}}{Q_{r}} \right)}^{2} + {\beta_{4}\left( {T_{ci} - T_{eo}} \right)} + {\beta_{5}\left( {T_{ci} - T_{eo}} \right)}^{2} + {\beta_{6}\left( {\left( {T_{ci} - T_{eo}} \right)\left( \frac{Q_{e}}{Q_{r}} \right)} \right)} + {\beta_{7}\left( {\left( {T_{ci} - T_{eo}} \right)\left( \frac{Q_{e}}{Q_{r}} \right)} \right)}^{2}}$

where the ratio of chiller load Q_(e) to chiller rated load Q_(r) is thepart load ratio (i.e., PLR=Q_(e)/Q_(r)) and the difference between thetemperature of the water entering the condenser T_(ci) and thetemperature of the water leaving the evaporator T_(eo) is the lift(i.e., Lift=T_(ci)−T_(eo)). The parameters β₁-β₇ are regression modelparameters and can be identified by fitting the model to a set oftraining data.

Still referring to FIG. 5, HVAC component models 510 are shown toinclude multivariate models 516. In some embodiments, multivariatemodels 516 include a multivariate polynomial model (MP). The MP modelwas used by the U.S. Department of Energy to do predictive modeling ofchillers. The MP model has a functional form of:

COP=β₁+β₂ Q _(e)+β₃ T _(ei)+β₄ T _(ci)+β₅ Q _(e) ²+β₆ T _(ei) ²+β₇ T_(ci) ²+β₈ Q _(e) T _(ei)+β₉ Q _(e) T _(ci)+β₁₀ T _(ei) T _(ci)

The MP model uses three independent variables, the evaporator (chiller)load Q_(e), the temperature of the water entering the evaporator T_(ei),and the temperature of the water entering the condenser T_(ci). The MPmodel uses seven parameters β₁-β₇ which can be identified by fitting themodel to a set of training data.

In some embodiments, multivariate models 516 include an invertedmultivariate polynomial model (MP-I). The MP-I model is the same as theMP model with the exception that it uses

$\frac{1}{COP}$

on the left hand side of the equation. The MP-I model has a functionalform of:

$\frac{1}{COP} = {\beta_{1} + {\beta_{2}Q_{e}} + {\beta_{3}T_{ei}} + {\beta_{4}T_{ci}} + {\beta_{5}Q_{e}^{2}} + {\beta_{6}T_{ei}^{2}} + {\beta_{7}T_{ci}^{2}} + {\beta_{8}Q_{e}T_{ei}} + {\beta_{9}Q_{e}T_{ci}} + {\beta_{10}T_{ei}T_{ci}}}$

The MP-I model uses three independent variables, the evaporator(chiller) load Q_(e), the temperature of the water entering theevaporator T_(ei), and the temperature of the water entering thecondenser T_(ci). The MP-I model uses seven parameters β₁-β₇ which canbe identified by fitting the model to a set of training data

Still referring to FIG. 5, HVAC component models 510 are shown toinclude other component models 518. Other component models 518 caninclude any type of HVAC component model other than Gordon-Ng models512, bi-quadratic models 514, and multivariate models 516. For example,other component models 518 can include Lee's simplified model (LS). TheLS model is based off of the NTU-ε method for heat exchangers, whichallows for the COP of a heat exchanger to be modeled without requiring ameasurement of the outlet temperatures for the condenser T_(co) orevaporator T_(eo). The LS model is derived from the first two laws ofthermodynamics and has a functional form of:

$\frac{1}{COP} = {{- 1} + \frac{T_{ci}}{T_{ei}} + {\frac{1}{Q_{e}}\left\lbrack {{- \beta_{1}} + {\beta_{2}T_{ci}} - {\beta_{3}\frac{T_{ci}}{T_{ei}}}} \right\rbrack}}$

which uses three variables, the evaporator (chiller) load Q_(e), thewater temperature entering the evaporator T_(ei), and the watertemperature entering the condenser T_(ci). The LS model also uses threeparameters β₁-β₃ which can be identified by fitting the model to a setof training data.

In some embodiments, other component models 518 include a simple linearregression model (SL). The SL model uses three independent variables andhas a functional form of:

COP=β₁ Q _(e)+β₂ T _(ei)+β₃ T _(ci)

where Q_(e) is the evaporator (chiller) load, T_(ei) is the temperatureof the water entering the evaporator, and T_(ci) is the temperature ofthe water entering the condenser. The SL model also uses threeparameters β₁-β₃ which can be identified by fitting the model to a setof training data.

In some embodiments, other component models 518 include an invertedsimple linear regression model (SL-I). The SL-I model is the same as theSL model with the exception that it uses

$\frac{1}{COP}$

on the left hand side of the equation. The SL-I model has a functionalform of:

$\frac{1}{COP} = {{\beta_{1}Q_{e}} + {\beta_{2}T_{ei}} + {\beta_{3}T_{ci}}}$

where Q_(e) is the evaporator (chiller) load, T_(ei) is the temperatureof the water entering the evaporator, and T_(ci) is the temperature ofthe water entering the condenser. The SL-I model also uses threeparameters β₁-β₃ which can be identified by fitting the model to a setof training data.

In some embodiments, each of HVAC component models 510 provides acomponent model prediction to prediction combiners 520. The componentmodel predictions can include a predicted value for a variable in HVACcomponent models 510 (e.g., COP). The predicted value can be calculatedas a function of the other variables in the HVAC component models 510.For example, each of HVAC component models 510 can use the correspondingmodel (i.e., the functional forms identified above) to solve for COP asa function of the other variables in the corresponding model (e.g.,T_(ci), T_(ei), Q_(e), etc.). In some embodiments, each of HVACcomponent models 510 provides a predicted value for the same variable.This allows prediction combiners 520 to combine the component modelpredictions using a systematic method to generate the combined modelprediction.

Prediction Combiners

Still referring to FIG. 5, predictive modeling system 402 is shown toinclude several prediction combiners 520. Prediction combiners 520 canbe configured to combine multiple component model predictions togenerate a single combined model prediction. For example, predictioncombiners 520 are shown receiving a plurality of component modelpredictions from HVAC component models 510. Prediction combiners 520 canuse any of a variety of techniques to combine the component modelpredictions (e.g., equal weighting, variance weighting, trimmed mean,etc.). Several of these techniques are described in detail below.

Prediction combiners 520 are shown to include an equal weightingcombiner 522. Equal weighting combiner 522 can combine multiplecomponent model predictions by calculating an equal-weight average ofthe multiple component model predictions. For example, equal weightingcombiner 522 can generate the combined model prediction ŷ by averagingmultiple component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) as shown in the following equation:

$\hat{y} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, {circumflex over (x)}_(i) isthe ith component model prediction, and N is the total number ofcomponent model predictions.

In some embodiments, equal weighting combiner 522 assigns an equalweight to each of the component model predictions. In some embodiments,the assigned weights sum to one. Accordingly, equal weighting combiner522 can calculate each weight by dividing the number one by the totalnumber of component model predictions, as shown in the followingequation:

$\begin{bmatrix}w_{1} & \ldots & w_{N}\end{bmatrix}^{T} = \frac{1}{N}$

where [w₁ . . . w_(N)]^(T) is a vector of the assigned weights and N isthe total number of component model predictions. In other embodiments,the assigned weights can sum to a number other than one. For example, ifunconstrained regression is used to combine the component modelpredictions, the assigned weights can sum to a number greater than oneor less than one.

Equal weighting combiner 522 can generate the combined model predictionŷ by calculating a weighted sum of the component model predictions{circumflex over (x)}₁ . . . {circumflex over (x)}_(N), as shown in thefollowing equation:

$\hat{y} = {\sum\limits_{i = 1}^{N}{w_{i}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, {circumflex over (x)}_(i) isthe ith component model prediction, and w_(i) is the calculated weightfor the ith component model prediction. Since all of the calculatedweights used by equal weighting combiner 522 are the same (e.g.,w_(i)=1/N), this equation is functionally equivalent to the previousequation for ŷ.

The equal weighting combination performed by equal weighting combiner522 has several advantages. For example, equal weighting is a simpletechnique and computationally inexpensive. Equal weighting can reducethe combined estimate error variance and often performs well. However,equal weighting does assign weights based on the performance of theindividual HVAC component models 510, which might yield improvedprediction.

Still referring to FIG. 5, prediction combiners 520 are shown to includea variance weighting combiner 524. Variance weighting combiner 524 cancombine multiple component predictions using a variance weightingtechnique. In some embodiments, variance weighting combiner 524 assignsa weight to each component model prediction {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) based on the error variance of thecorresponding HVAC component model 510. For example, variance weightingcombiner 524 can calculate a weight for each component model predictionusing the following equation:

$w_{i} = \frac{\frac{1}{\sigma_{i}^{2}}}{\sum\limits_{i = 1}^{N}\frac{1}{\sigma_{i}^{2}}}$

where w_(i) is the weight assigned to the ith component modelprediction, σ_(i) ² is the error variance of the ith component model'spredictions, and N is the total number of component model predictions.

The numerator in the preceding equation is the inverse variance of theith component model's predictions, whereas the denominator of thisequation is the summation of the inverse variances of all the componentmodels' predictions. Accordingly, each weight calculated by varianceweighting combiner 524 may be inversely proportional to the variance ofthe corresponding component model's predictions (i.e., w_(i)∝1/σ_(i) ²)and the summation of the weights may be equal to one (i.e., Σ_(i=1) ^(N)w_(i)=1). This formulation assumes that the component model predictions{circumflex over (x)}₁ . . . {circumflex over (x)}_(N) are independentand have zero covariance, which in practice is a reasonable assumption.In some embodiments, variance weighting combiner 524 uses the standarddeviation σ_(i) instead of the variance σ_(i) ² when calculating theassigned weights.

In some embodiments, variance weighting combiner 524 calculates thevariance σ_(i) ² for the ith HVAC component model 510 as a function ofhow well the component model predictions {circumflex over (x)}_(i) fitthe actual values of the predicted variable y. For example, varianceweighting combiner 524 can calculate the variance σ_(i) ² as aregression statistic for the ith HVAC component model 510 when the HVACcomponent model is trained or fit to a set of training data. Theregression statistic can include, for example, the mean squared error,standard error, error variance, or other indication of how well thecomponent model predictions {circumflex over (x)}_(i) generated by theith HVAC component model fit the actual values of the predicted variabley. Larger values of the regression statistic or variance σ_(i) ² mayindicate a relatively worse fit (i.e., worse prediction accuracy),whereas smaller values of the regression statistic or variance σ_(i) ²may indicate a relatively better fit (i.e., better prediction accuracy).Variance weighting combiner 524 can repeat this process for each HVACcomponent models 510 to generate a corresponding variance σ_(i) ² foreach HVAC component model 510.

In some embodiments, variance weighting combiner 524 calculates thevariance σ_(i) ² for the ith HVAC component model 510 as a function ofthe uncertainty associated with the component model prediction{circumflex over (x)}_(i). For example, the component model prediction{circumflex over (x)}_(i) may be a calculated value based on one or moremeasured values (e.g., T_(ci), T_(ei), T_(eo), etc.), calculated values,or other model parameters. Each of the inputs to the HVAC componentmodels 510 can have an uncertainty associated therewith (e.g.,measurement uncertainty, process uncertainty, etc.). Variance weightingcombiner 524 can calculate the uncertainty of the component modelprediction {circumflex over (x)}_(i) as a function of the uncertaintiesassociated with each the inputs to the HVAC component model. In someembodiments, variance weighting combiner 524 uses the uncertainty of thecomponent model prediction {circumflex over (x)}_(i) as the varianceσ_(i) ². Accordingly, predictions that are less certain (i.e., higheruncertainty) can be assigned a lesser weight, whereas predictions thatare more certain (i.e., lower uncertainty) can be assigned a greaterweight. Variance weighting combiner 524 can repeat this process for eachHVAC component models 510 to generate a corresponding variance σ_(i) ²for each HVAC component model 510.

Variance weighting combiner 524 can generate the combined modelprediction ŷ by calculating a weighted sum of the component modelpredictions {circumflex over (x)}₁ . . . {circumflex over (x)}_(N), asshown in the following equation:

$\hat{y} = {\sum\limits_{i = 1}^{N}{w_{i}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, {circumflex over (x)}_(i) isthe ith component model prediction, and w_(i) is the calculated weightfor the ith component model prediction. The variance weighting techniqueis simple and computationally inexpensive. Advantageously, the varianceweighting technique can reduce the combined estimate error variancerelative to the equal weighting technique by assigning greater weightsto more accurate or more certain component model predictions and lesserweights to less accurate or less certain component model predictions.

Still referring to FIG. 5, prediction combiners 520 are shown to includea trimmed mean combiner 526. Trimmed mean combiner 526 can be configuredto generate the combined model prediction using a trimmed meancombination technique. In some embodiments, trimmed mean combiner 526receives a set of component model predictions from HVAC component models510 and identifies the value (e.g., numerical value) of each componentmodel prediction. Trimmed mean combiner 526 can generate a trimmed orfiltered subset of the component model predictions by removing one ormore of the component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) from the initial set.

In some embodiments, trimmed mean combiner 526 selectively removes apredetermined number of the highest and/or lowest component modelpredictions from the initial set of component model predictions togenerate the trimmed or filtered subset. For example, trimmed meancombiner 526 can remove one or more of the highest component modelpredictions (e.g., single highest, two highest, three highest, etc.)and/or one or more of the lowest component model predictions (e.g.,single lowest, two lowest, three lowest, etc.) from the initial set ofcomponent model predictions. In other embodiments, trimmed mean combiner526 removes one or more of the component model predictions that qualifyas outliers relative to the others. For example, trimmed mean combiner526 can remove one or more of the component model predictions thatdeviate from the mean of the initial set by a predetermined threshold(e.g., two standard deviations, three standard deviations, apredetermined percentage of the mean, etc.).

After the initial set of component model predictions has been trimmed orfiltered by removing one or more of the component model predictions,trimmed mean combiner 526 can generate the combined model predictionusing the remaining component model predictions in the trimmed orfiltered subset. In some embodiments, trimmed mean combiner 526 uses theequal weighting technique or variance weighting technique describedabove to combine the component model predictions in the filtered subset.Advantageously, trimmed means combiner 526 can improve the accuracy ofthe combined model prediction by discarding the predictions from theworst performing models, which are likely to have the highest or lowestvalues. The trimmed means technique is computationally inexpensive androbust to outliers in the set of component model predictions.

Although only a few prediction combiners 520 are described in detail, itshould be understood that prediction combiners 520 can include any typeof combiner configured to generate a combined prediction by combiningthe predictions of multiple component models. For example, predictioncombiners 520 are shown to include other combiners 528. Other combiners528 can use any of a variety of combining techniques (e.g., principalcomponents, constrained or unconstrained regression, artificial neuralnetworks, ensemble machine learning techniques (e.g., boosting, bagging,etc.), to generate a combined model prediction from multiple componentmodel predictions.

Model Evaluation and Selection

Still referring to FIG. 5, predictive modeling system 402 is shown toinclude a model evaluator 532. Model evaluator 532 can be configured toevaluate the performance of HVAC component models 510 and predictioncombiners 520 by comparing the model-predicted values (e.g., {umlautover (x)}₁ . . . {circumflex over (x)}_(N) and ŷ) to the actual values yof the predicted variable. In some embodiments, model evaluator 532trains each of HVAC component models 510 by fitting each model to a setof training data. For example, model evaluator 532 can use a regressiontechnique (e.g., linear regression, non-linear regression, polynomialregression, ridge regression, least squares regression, etc.) toidentify values for the model coefficients of HVAC component models 510(e.g., β₁, β₂, β₃, etc.). The set of training data can include valuesfor each of the input variables to HVAC component models 510 andcorresponding values for the predicted variable at each of a pluralityof time steps. In some embodiments, the training data is defined by adata window having a predetermined duration (e.g., 60 days).

In some embodiments, model evaluator 532 uses a first portion of thetraining data to train HVAC component models 510 and a second portion ofthe training data to evaluate model performance. For example, modelevaluator 532 can fit each of HVAC component models 510 to the trainingdata in a first portion of the data window (e.g., first 30 days of data)to identify values for the model coefficients Model evaluator 532 canthen apply the trained HVAC component models 510 to the training data inthe second portion of the data window (e.g., second 30 days of data) togenerate the component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) as a function of the input variables (e.g.,T_(ci), T_(ei), T_(eo), etc.). The component model predictions can thenbe used by prediction combiners 520 to predict values for theperformance variable ŷ (e.g., COP).

In some embodiments, the first portion of the data window is a trainingperiod and the second portion of the data window is an evaluationperiod. HVAC component models 510 can generate component modelpredictions {circumflex over (x)}₁ . . . {circumflex over (x)}_(N) foreach time step in the evaluation period. Similarly, prediction combiners520 generate a predicted value of the performance variable ŷ for eachtime step in the evaluation period. For example, samples of themonitored variables can be collected every fifteen minutes which resultsin a total of 96 samples per day or 2880 samples over the duration of a30 day evaluation period. This will result in 2880 predicted values ofthe performance variable ŷ over the duration of the evaluation period.Of course, the sampling intervals and durations of the training periodand evaluation period can vary depending on the particularimplementation. In general, prediction combiners 520 can generate a setof n predicted values for the performance variable ŷ, where n is thetotal number of samples in the evaluation period.

In some embodiments, model evaluator 532 uses a sliding data window totrain and evaluate HVAC component models 510. For example, the datawindow can be shifted forward in time by a predetermined amount (e.g.,one day) to define a new set of training data. Both the training andevaluation steps can be repeated iteratively each time the data windowis shifted. The sliding data window and iterative prediction/evaluationtechnique are described in greater detail with reference to FIG. 7.

Model evaluator 532 can be configured to evaluate the combined modelpredictions 9 generated by each of prediction combiners 520 relative tothe actual values y of the predicted variable. For example, modelevaluator 532 can calculate the mean absolute percentage error (MAPE) ofeach prediction combiner 520 using the following equation:

${MAPE}_{i} = {100 \times \frac{\sum\limits_{j = 1}^{n}{\frac{{\hat{y}}_{j} - y_{j}}{y_{j}}}}{n}\mspace{14mu} \%}$

where MAPE_(i) is the mean absolute percentage error of the ithprediction combiner 520, ŷ_(J) is the predicted value of the performancevariable for the jth sample in the evaluation period, and y_(j) is theactual value of the performance variable for the jth sample in theevaluation period. The MAPE value for a given prediction combiner 520indicates the average error of the prediction combiner 520 over theduration of the evaluation period. For example, a value of MAPE=5%indicates that the predicted values ŷ₁ . . . ŷ_(n) generated by the ithprediction combiner 520 had an average prediction error of 5% relativeto the actual values of the performance variable y₁ . . . y_(n) over theduration of the evaluation period.

Model evaluator 532 can use any of a variety of metrics to evaluate thecombined model predictions ŷ generated by each of prediction combiners520 relative to the actual values y of the predicted variable. Forexample, model evaluator 532 can calculate the root mean square error(RMSE), normalized root mean square error (NRMSE), coefficient ofvariation of the root mean square error (CVRMSE), or any other metric toevaluate the combined model predictions. Although MAPE is described asthe primary evaluation metric, it should be understood that any otherevaluation metric can be used in various other embodiments.

In some embodiments, model evaluator 532 generates a score for each ofprediction combiners 520 based on a result of the evaluation. Forexample, model evaluator 532 can assign a score to each of predictioncombiners 520 based on the MAPE values for each prediction combiner 520.In some embodiments, the score is an accuracy score. Model evaluator 532can assign higher accuracy scores to prediction combiners 520 withsmaller MAPE values, and lower accuracy scores to prediction combiners520 with larger MAPE values. The accuracy scores may indicate which ofprediction combiners 520 produced the most accurate predictions, onaverage, over the duration of the evaluation period.

Still referring to FIG. 5, predictive modeling system 402 is shown toinclude a combiner selector 530. Combiner selector 530 is shownreceiving scores from model evaluator 532. The scores can be MAPEscores, accuracy scores, or any other scores which indicate theprediction accuracy of prediction combiners 520. In some embodiments,combiner selector 530 is configured to select one or more of predictioncombiners 520 based on the assigned scores. For example, combinerselector 530 can select the prediction combiner 520 with the lowest MAPEscore or the highest accuracy score. In some embodiments, predictivemodeling system 402 is configured to use the selected predictioncombiner 520 to generate the combined model prediction. For example,predictive modeling system 402 can activate or enable the selectedprediction combiner 520 and deactivate or disable the non-selectedprediction combiners 520.

In some embodiments, predictive modeling system 402 periodicallyreactivates all of the inactive prediction combiners 520 and reevaluatestheir performance to determine whether a different prediction combiner520 has become more accurate. For example, some of prediction combiners520 may be more accurate under some operating conditions (e.g., highload conditions) and less accurate under other operating conditions(e.g., low load conditions). Model evaluator 532 can reevaluate theperformance of each prediction combiner 520 at regular intervals or inresponse to an event (e.g., the HVAC equipment transitioning into adifferent operating mode or state) to determine whether a differentprediction combiner 520 would be more accurate than thepreviously-selected prediction combiner 520.

Example Chiller and Component Model Variables

Referring now to FIG. 6, a schematic diagram of a chiller 600 is shown,according to an exemplary embodiment. Chiller 600 is an example of atype of HVAC equipment 340 which can provide monitored variables andoperating points to predictive modeling system 402. Chiller 600 is shownto include a refrigeration circuit having a condenser 602, an expansionvalve 604, an evaporator 606, a compressor 608, and a control panel 610.In some embodiments, chiller 600 includes sensors that measure a set ofmonitored variables at various locations along the refrigerationcircuit. Predictive modeling system 402 can use these or other variablesas inputs to various component models 510 to generate component modelpredictions.

Table 1 below includes an exemplary set of chiller variables that can beused in component models 510. The component model variables can includemonitored variables measured by sensors in chiller 600. For example, thewater temperature entering the condenser T_(ci), the water temperatureentering the evaporator T_(ei), and the water temperature leaving theevaporator T_(eo) can be measured by temperature sensors locatedupstream and downstream of condenser 602 and evaporator 606. Themonitored variables can be received from various components of centralplant system 300 via communications interface 502 and provided as inputsto component models 510.

TABLE 1 Chiller Component Model Variables Variable Description COPCoefficient of performance T_(ci) Water temperature entering condenserT_(ei) Water temperature entering evaporator T_(eo) Water temperatureleaving evaporator Q_(e) Evaporator (chiller) load Q_(r) Chiller ratedload {dot over (m)}_(c) Mass flow rate of condenser (cooling) water {dotover (m)}_(e) Mass flow rate of evaporator (chilled) water cp_(c) Heatcapacity of water at condenser temperature cp_(e) Heat capacity of waterat evaporator temperature

The component model variables can also include calculated variables. Thecalculated variables can be calculated based on one or more of themeasured variables and/or other input variables received by predictivemodeling system 402. For example, the mass flow rate of the condenser(cooling) water {dot over (m)}_(c) and the mass flow rate of theevaporator (chilled) water {dot over (m)}_(e) can be calculated based onflow rate measured by one or more flow sensors of chiller 600.Similarly, the heat capacity of the water at the condenser temperaturecp_(c) and the heat capacity of the water at the evaporator temperaturecp_(e) can be calculated based on the measured temperatures and knownproperties of water. The calculated variables can be calculated bypredictive modeling system 402 based on the measured variables and/orreceived as inputs via communications interface 502.

The component model variables can also include fixed variables such asthe chiller rated load Q_(r) or other input variables such as theevaporator (chiller) load Q_(e). The chiller rated load Q_(r) can bereceived as an input from chiller 600, BAS 308, or other systems ordevices in central plant system 300. The evaporator load Q_(e) can be anactual or planned thermal energy load for chiller 600. In someembodiments, the evaporator load Q_(e) is provided by central plantcontroller 302 as an operating point or equipment setpoint. Thecomponent model variables can also include component model predictionssuch as the coefficient of performance COP, resource consumption, powerconsumption, or other predictions which can be provided as outputs ofcomponent models 510.

Sliding Data Window

Referring now to FIG. 7, several graphs 710, 720, and 730 illustrating asliding data window and iterative prediction technique which can be usedby predictive modeling system 402 are shown, according to an exemplaryembodiment. In all three graphs 710-730, line 702 represents the actualvalue of the performance variable y (e.g., actual chiller efficiency).Line 704 represents the model-predicted value of the performancevariable ŷ generated by prediction combiners 520 (e.g., predictedchiller efficiency). Line 706 represents a Naïve value of theperformance variable, which has a constant value (e.g., constant chillerefficiency).

In graph 710, the sliding data window is shown to include a trainingperiod 712 and an evaluation period 714. In some embodiments, trainingperiod 712 spans the first 30 days (e.g., days 1-30), whereas evaluationperiod 714 spans the second 30 days (e.g., days 31-60). However, itshould be understood that training period 712 and evaluation period 714can have any duration. During training period 712, model evaluator 532uses samples of the monitored variables to train HVAC component models510. Training HVAC component models 510 can include identifying valuesfor the model coefficients β. For example, model evaluator 532 can use aregression technique to calculate the model coefficients β based on thevalues of the monitored variables (e.g., T_(ci), T_(ei), T_(eo), etc.)and the corresponding values of the performance variable y duringtraining period 712.

Model evaluator 532 can then apply the trained HVAC component models 510to values of the monitored variables during evaluation period 714 togenerate component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) for each time step in evaluation period 714.The component model predictions can then be used by prediction combiners520 to predict values for the performance variable ŷ for each time stepin evaluation period 714. The remaining days 716 are not used during thefirst iteration shown in graph 710.

In graph 720, the sliding data window is shifted forward by apredetermined duration (e.g., 1 day) to define a new training period 722and a new evaluation period 724. Training data from time period 721(e.g., the first day) is not included in either training period 722 orevaluation period 724. In some embodiments, training period 722 spans a30 day period following time period 721 (e.g., days 2-31), whereasevaluation period 724 spans a 30 day period following training period722 (e.g., days 32-61). During training period 722, model evaluator 532uses samples of the monitored variables to train HVAC component models510.

Model evaluator 532 can then apply the trained HVAC component models 510to values of the monitored variables during evaluation period 724 togenerate component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) for each time step in evaluation period 724.The component model predictions can then be used by prediction combiners520 to predict values for the performance variable ŷ for each time stepin evaluation period 724. The remaining days 726 are not used during thesecond iteration shown in graph 720.

In graph 730, the sliding data window is shifted forward again by thepredetermined duration (e.g., 1 day) to define a new training period 732and a new evaluation period 734. Training data from time period 731(e.g., the first two days) is not included in either training period 732or evaluation period 734. In some embodiments, training period 732 spansa 30 day period following time period 731 (e.g., days 3-32), whereasevaluation period 734 spans a 30 day period following training period732 (e.g., days 33-62). During training period 732, model evaluator 532uses samples of the monitored variables to train HVAC component models510.

Model evaluator 532 can then apply the trained HVAC component models 510to values of the monitored variables during evaluation period 734 togenerate component model predictions {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) for each time step in evaluation period 734.The component model predictions can then be used by prediction combiners520 to predict values for the performance variable ŷ for each time stepin evaluation period 734. The remaining days 736 are not used during thesecond iteration shown in graph 730. This process can be repeated untilthe evaluation window reaches the end of the time period for whichtraining data has been collected.

Flow Diagrams

Referring now to FIG. 8, a flowchart of a process 800 for controllingHVAC equipment is shown, according to an exemplary embodiment. Process800 can be performed by one or more components of central plant system300. For example, process 800 can be performed by controller 302,predictive modeling system 402, BAS 308, and/or HVAC equipment 340, asdescribed with reference to FIGS. 3-5.

Process 800 is shown to include determining an operating point for HVACequipment 340 (step 802). In some embodiments, the operating point is asetpoint for HVAC equipment 340. For example, the operating point can bea load setpoint, a capacity setpoint, a setpoint for a variable affectedby HVAC equipment 340, a mode setpoint, an operating state, an on/offdecision, or any other variable which indicates the current operatingstate or condition of HVAC equipment 340. In some embodiments, theoperating point is the result of an optimization procedure. For example,the operating point can be calculated by high level optimizer 330 or lowlevel optimizer 332, as previously described.

In some embodiments, step 802 includes receiving one or more monitoredvariables associated with the operating point. The monitored variablescan include measured variables (e.g., measured temperature, measured airflow rate, etc.), calculated variables (e.g., heat capacity of asubstance at a given temperature, enthalpy, coefficient of performance,etc.), control variables (e.g., setpoints, equipment operating points,on/off decisions, etc.), equipment parameters (e.g., rated load, controlparameters, etc.), or any other variables that characterize theoperation of HVAC equipment 340. In some embodiments, the monitoredvariables are measured by one or more sensors associated with HVACequipment 340.

Process 800 is shown to include generating a plurality of componentmodel predictions based on the operating point (step 804). In someembodiments, each of the component model predictions is a predictedvalue of a performance variable indicating a predicted performance ofHVAC equipment 340 at the operating point. For example, the operatingpoint can be a setpoint for HVAC equipment 340 and the performancevariable can indicate a predicted power consumption of HVAC equipment340 at the setpoint. Each of the component model predictions can begenerated by one of HVAC component models 510. In some embodiments, eachof HVAC component models 510 has a different functional form and uses adifferent mathematical relationship to generate the correspondingcomponent model prediction.

HVAC component models 510 can include any of a variety of predictivemodels configured to predict the performance of a HVAC component basedon a set of input variables (e.g., monitored variables and/or operatingpoints). In some embodiments, each of HVAC component models 510corresponds to a particular HVAC device, a particular type of HVACdevice (e.g., a chiller, a boiler, an actuator, etc.) or a particularmodel of HVAC device (e.g., chiller model A, chiller model B, etc.) andcan be used to predict the performance of the corresponding HVAC device,device type, or model. For example, HVAC component models 510 caninclude power consumption models that can be used to predict the powerconsumption of various HVAC devices. In some embodiments, HVAC componentmodels 510 define power consumption as a function of equipment loadand/or equipment setpoints. For example, the HVAC component model for achiller may define the power consumption of the chiller as a function ofcold water production and/or chiller load setpoints.

In some embodiments, HVAC component models 510 define the relationshipbetween the inputs to a HVAC device and the outputs of the HVAC device.HVAC component models 510 can be used to predict an amount of inputresources (e.g., electricity, water, natural gas, etc.) required toproduce a desired amount of an output resource (e.g., chilled water, hotwater, electricity, etc.). HVAC component models 510 can be used by lowlevel optimizer 332 to predict the power consumption of various devicesof HVAC equipment 340 that will result from the on/off decisions andsetpoints selected by low level optimizer 332.

In some embodiments, HVAC component models 510 are configured to predictperformance-related variables (e.g., coefficient of performance, powerconsumption, etc.) of HVAC equipment 340 as a function of the monitoredvariables and/or operating points. In some embodiments, HVAC componentmodels 510 define the coefficient of performance of a HVAC device as afunction of various input variables. For example, the HVAC componentmodel for a chiller may define the chiller's coefficient of performanceCOP as a function of the water temperature entering the chiller'scondenser T_(ci), the water temperature entering the chiller'sevaporator T_(ei), the water temperature leaving the chiller'sevaporator T_(eo), the evaporator (chiller) load Q_(e), the chillerrated load Q_(r), the mass flow rate of condenser (cooling) water {dotover (m)}_(e), the mass flow rate of evaporator (chilled) water {dotover (m)}_(e), the heat capacity of water at condenser temperaturecp_(c), the heat capacity of water at evaporator temperature cp_(e),and/or other variables that can be provided as inputs to HVAC componentmodels 510.

In some embodiments, HVAC component models 510 include multiplepredictive models for each HVAC device of HVAC equipment 340. Each ofHVAC component models 510 may predict the same variable using adifferent prediction technique. For example, HVAC component models 510are shown to include Gordon-Ng models 512, bi-quadratic models 514,multivariate models 516, and other models 518. Gordon-Ng models 512 canbe configured to predict the value of a performance variable (e.g.,coefficient of performance, power consumption, etc.) using a Gordon-Ngprediction technique. Similarly, bi-quadratic models 514 can beconfigured to predict the value of the same performance variable using abi-quadratic prediction technique, and multivariate models 516 can beconfigured to predict the value of the same performance variable using amultivariate prediction technique. These and several other predictiontechniques which can be used by HVAC component models 510 are describedin greater detail with reference to FIG. 5.

Each of HVAC component models 510 can be configured to predict the sameperformance variable. For example, each of HVAC component models 510 fora chiller can independently predict the coefficient of performance ofthe chiller, resulting in multiple independent predictions. DifferentHVAC component models 510 can use the same set of input variables ordifferent sets of input variables to perform their predictions. Each ofthe predictions generated by HVAC component models 510 (i.e., thecomponent model predictions) can be provided as an output to predictioncombiners 520.

Still referring to FIG. 8, process 800 is shown to include combining theplurality of component model predictions to form a combined modelprediction (step 806). The combined model prediction can be generated byprediction combiners 520 and can include another value of theperformance variable. Prediction combiners 520 can use any of a varietyof techniques to combine the component model predictions (e.g., equalweighting, variance weighting, trimmed mean, etc.). For example, step806 can include using equal weighting combiner 522 to combine multiplecomponent model predictions by calculating an equal-weight average ofthe multiple component model predictions. Equal weighting combiner 522can generate the combined model prediction ŷ by averaging multiplecomponent model predictions {circumflex over (x)}₁ . . . {circumflexover (x)}_(N), as shown in the following equation:

$\hat{y} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, {circumflex over (x)}_(i) isthe ith component model prediction, and N is the total number ofcomponent model predictions.

In some embodiments, step 806 includes assigning an equal weight to eachof the component model predictions. In some embodiments, the assignedweights sum to one. Accordingly, each weight can be calculated bydividing the number one by the total number of component modelpredictions, as shown in the following equation:

$\begin{bmatrix}w_{1} & \ldots & w_{N}\end{bmatrix}^{T} = \frac{1}{N}$

where [w₁ . . . w_(N)]^(T) is a vector of the assigned weights and N isthe total number of component model predictions. In other embodiments,the assigned weights can sum to a number other than one. For example, ifunconstrained regression is used to combine the component modelpredictions, the assigned weights can sum to a number greater than oneor less than one.

Step 806 can include generating the combined model prediction ŷ bycalculating a weighted sum of the component model predictions{circumflex over (x)}₁ . . . {circumflex over (x)}_(N) as shown in thefollowing equation:

$\hat{y} = {\sum\limits_{i = 1}^{N}{w_{i}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, {circumflex over (x)}_(i) isthe ith component model prediction, and w_(i) is the calculated weightfor the ith component model prediction. Since all of the calculatedweights used by equal weighting combiner 522 are the same (e.g.,w_(i)=1/N), this equation is functionally equivalent to the previousequation for ŷ.

The equal weighting combination has several advantages. For example,equal weighting is a simple technique and computationally inexpensive.Equal weighting can reduce the combined estimate error variance andoften performs well. However, equal weighting does assign weights basedon the performance of the individual HVAC component models 510, whichmight yield improved prediction.

In some embodiments, step 806 includes using variance weighting combiner524 to combine the component model predictions. Variance weightingcombiner 524 can combine multiple component predictions using a varianceweighting technique. In some embodiments, step 806 includes assigning aweight to each component model prediction {circumflex over (x)}₁ . . .{circumflex over (x)}_(N) based on the error variance of thecorresponding HVAC component model 510. For example, step 806 caninclude calculating a weight for each component model prediction usingthe following equation:

$w_{i} = \frac{\frac{1}{\sigma_{i}^{2}}}{\sum\limits_{i = 1}^{N}\frac{1}{\sigma_{i}^{2}}}$

where w_(i) is the weight assigned to the ith component modelprediction, σ_(i) ² is the error variance of the ith component model'spredictions, and N is the total number of component model predictions.

The numerator in the preceding equation is the inverse variance of theith component model's predictions, whereas the denominator of thisequation is the summation of the inverse variances of all the componentmodels' predictions. Accordingly, each weight calculated in step 806 maybe inversely proportional to the variance of the corresponding componentmodel's predictions (i.e., w_(i) ∝1/σ_(i) ²) and the summation of theweights may be equal to one (i.e., Σ_(i=1) ^(N) w_(i)=1). Thisformulation assumes that the component model predictions {circumflexover (x)}₁ . . . {circumflex over (x)}_(N) are independent and have zerocovariance, which in practice is a reasonable assumption. In someembodiments, step 806 includes using the standard deviation σ_(i)instead of the variance σ_(i) ² when calculating the assigned weights.

In some embodiments, step 806 includes using the variance σ_(i) ² forthe ith HVAC component model 510 as a function of how well the componentmodel predictions {circumflex over (x)}_(i) fit the actual values of thepredicted variable y. For example, step 806 can include calculating thevariance σ_(i) ² as a regression statistic for the ith HVAC componentmodel 510 when the HVAC component model is trained or fit to a set oftraining data. The regression statistic can include, for example, themean squared error, standard error, error variance, or other indicationof how well the component model predictions {circumflex over (x)}_(i)generated by the ith HVAC component model fit the actual values of thepredicted variable y. Larger values of the regression statistic orvariance σ_(i) ² may indicate a relatively worse fit (i.e., worseprediction accuracy), whereas smaller values of the regression statisticor variance σ_(i) ² may indicate a relatively better fit (i.e., betterprediction accuracy). Step 806 can include repeating this process foreach HVAC component models 510 to generate a corresponding varianceσ_(i) ² for each HVAC component model 510.

In some embodiments, step 806 includes calculating the variance σ_(i) ²for the ith HVAC component model 510 as a function of the uncertaintyassociated with the component model prediction {circumflex over(x)}_(i). For example, the component model prediction {circumflex over(x)}_(i) may be a calculated value based on one or more measured values(e.g., T_(ci), T_(ei), T_(eo), etc.), calculated values, or other modelparameters. Each of the inputs to the HVAC component models 510 can havean uncertainty associated therewith (e.g., measurement uncertainty,process uncertainty, etc.). Step 806 can include calculating theuncertainty of the component model prediction {circumflex over (x)}_(i)as a function of the uncertainties associated with each the inputs tothe HVAC component model. In some embodiments, step 806 includes usingthe uncertainty of the component model prediction {circumflex over(x)}_(i) as the variance σ_(i) ². Accordingly, predictions that are lesscertain (i.e., higher uncertainty) can be assigned a lesser weight,whereas predictions that are more certain (i.e., lower uncertainty) canbe assigned a greater weight. Step 806 can include repeating thisprocess for each HVAC component models 510 to generate a correspondingvariance σ_(i) ² for each HVAC component model 510.

Step 806 can include generating the combined model prediction ŷ bycalculating a weighted sum of the component model predictions{circumflex over (x)}₁ . . . {circumflex over (x)}_(N) as shown in thefollowing equation:

$\hat{y} = {\sum\limits_{i = 1}^{N}{w_{i}{\hat{x}}_{i}}}$

where ŷ is the combined model prediction, is the ith component modelprediction, and w_(i) is the calculated weight for the ith componentmodel prediction. The variance weighting technique is simple andcomputationally inexpensive. Advantageously, the variance weightingtechnique can reduce the combined estimate error variance relative tothe equal weighting technique by assigning greater weights to moreaccurate or more certain component model predictions and lesser weightsto less accurate or less certain component model predictions.

In some embodiments, step 806 includes using trimmed mean combiner 526to combine the component model predictions. Trimmed mean combiner 526can be configured to generate the combined model prediction using atrimmed mean combination technique. In some embodiments, step 806includes receiving a set of component model predictions {circumflex over(x)}₁ . . . {circumflex over (x)}_(N) from HVAC component models 510 andidentifies the value (e.g., numerical value) of each component modelprediction. Step 806 can include generating a trimmed or filtered subsetof the component model predictions by removing one or more of thecomponent model predictions {circumflex over (x)}₁ . . . {circumflexover (x)}_(N) from the initial set.

In some embodiments, step 806 includes selectively removing apredetermined number of the highest and/or lowest component modelpredictions from the initial set of component model predictions togenerate the trimmed or filtered subset. For example, step 806 caninclude removing one or more of the highest component model predictions(e.g., single highest, two highest, three highest, etc.) and/or one ormore of the lowest component model predictions (e.g., single lowest, twolowest, three lowest, etc.) from the initial set of component modelpredictions. In other embodiments, step 806 includes removing one ormore of the component model predictions that qualify as outliersrelative to the others. For example, step 806 can include removing oneor more of the component model predictions that deviate from the mean ofthe initial set by a predetermined threshold (e.g., two standarddeviations, three standard deviations, a predetermined percentage of themean, etc.).

After the initial set of component model predictions has been trimmed orfiltered by removing one or more of the component model predictions,step 806 can include generating the combined model prediction using theremaining component model predictions in the trimmed or filtered subset.In some embodiments, step 806 includes using the equal weightingtechnique or variance weighting technique described above to combine thecomponent model predictions in the filtered subset. Advantageously, step806 can improve the accuracy of the combined model prediction bydiscarding the predictions from the worst performing models, which arelikely to have the highest or lowest values. The trimmed means techniqueis computationally inexpensive and robust to outliers in the set ofcomponent model predictions.

Still referring to FIG. 8, process 800 is shown to include using thecombined model prediction to optimize the operating point (step 808).Step 808 can be performed by one or more components of controller 302.For example, if the combined model prediction is an estimated amount ofpower consumption, low level optimizer 332 can optimize the operatingpoint by selecting an operating point which minimizes the estimatedamount of power consumption. Low level optimizer 332 can combine theestimated power consumptions for multiple devices of HVAC equipment 340to generate a subplant curve for an entire subplant. High leveloptimizer 330 can use the subplant curves to allocate thermal energyloads to various subplants. The allocated thermal energy loads can thenbe used by low level optimizer 332 to determine an optimal operatingpoint for HVAC equipment 340. For example, low level optimizer 332 canuse the allocated thermal energy load for a subplant to select optimaloperating points for the HVAC equipment 340 within the subplant. In someembodiments, the optimal operating points minimize the amount of powerconsumed by the subplant to satisfy the thermal energy load.

Process 800 is shown to include operating the HVAC equipment at theoptimized operating point (step 810). Step 810 can include providing asetpoint to HVAC equipment 340 or otherwise controlling the operation ofHVAC equipment 340 to achieve the optimized operating point. HVACequipment 340 can be configured to affect an environmental conditionwithin a building. The environmental condition can include, for example,building temperature, humidity, air flow, air quality, lighting, orother conditions in the building. Step 810 can include operating theHVAC equipment 340 to achieve a setpoint value for the environmentalcondition or to maintain the environmental condition within a range ofvalues. For example, step 810 can include operating the HVAC equipment340 to maintain building temperature within a predetermined temperaturerange. In some embodiments, the environmental condition is used as aconstraint on an optimization procedure such that the HVAC equipment 340is operated to minimize energy consumption or energy cost whilemaintaining the environmental condition within a predetermined range ofvalues.

Referring now to FIG. 9, a flowchart of a process 900 for evaluatingmodel performance and selecting one of prediction combiners 520 isshown, according to an exemplary embodiment. Process 900 can beperformed by one or more components of central plant system 300. Forexample, process 900 can be performed by controller 302, predictivemodeling system 402, BAS 308, and/or HVAC equipment 340, as describedwith reference to FIGS. 3-5.

Process 900 is shown to include training a plurality of HVAC componentmodels using training data in a first portion of a data window (step902). In some embodiments, step 902 is performed by model evaluator 532,as described with reference to FIG. 5. Step 902 can include trainingeach of HVAC component models 510 by fitting each model to a set oftraining data. For example, step 902 can include using a regressiontechnique (e.g., linear regression, non-linear regression, polynomialregression, ridge regression, least squares regression, etc.) toidentify values for the model coefficients of HVAC component models 510(e.g., β₁, β₂, β₃, etc.). The set of training data can include valuesfor each of the input variables to HVAC component models 510 andcorresponding values for the predicted variable at each of a pluralityof time steps. In some embodiments, the training data is defined by adata window having a predetermined duration (e.g., 60 days).

Process 900 is shown to include generating a plurality of componentmodel predictions for a second portion of the data window using the HVACcomponent models (step 904) and combining the plurality of componentmodel predictions using a plurality of prediction combiners to form aplurality of combined model predictions for the second portion of thedata window (step 906). In some embodiments, process 900 includes usinga first portion of the training data to train HVAC component models 510and a second portion of the training data to evaluate model performance.For example, step 902 can include fitting each of HVAC component models510 to the training data in a first portion of the data window (e.g.,first 30 days of data) to identify values for the model coefficients β.Step 904 can then apply the trained HVAC component models 510 to thetraining data in the second portion of the data window (e.g., second 30days of data) to generate the component model predictions {circumflexover (x)}₁ . . . {circumflex over (x)}_(N) as a function of the inputvariables (e.g., T_(ci), T_(ei), T_(eo), etc.). The component modelpredictions can then be used in step 906 to predict values for theperformance variable ŷ (e.g., COP).

In some embodiments, the first portion of the data window is a trainingperiod and the second portion of the data window is an evaluationperiod. Step 904 can generate component model predictions {circumflexover (x)}₁ . . . {circumflex over (x)}_(N) for each time step in theevaluation period. Similarly, step 906 can generate a predicted value ofthe performance variable ŷ for each time step in the evaluation period.For example, samples of the monitored variables can be collected everyfifteen minutes which results in a total of 96 samples per day or 2880samples over the duration of a 30 day evaluation period. This willresult in 2880 predicted values of the performance variable ŷ over theduration of the evaluation period. Of course, the sampling intervals anddurations of the training period and evaluation period can varydepending on the particular implementation. In general, step 906 cangenerate a set of n predicted values for the performance variable ŷ,where n is the total number of samples in the evaluation period.

Still referring to FIG. 9, process 900 is shown to include calculating ascore for each of the prediction combiners by comparing the combinedmodel predictions to actual values of the predicted variable in thesecond portion of the data window (step 908). Step 908 can includeevaluating the combined model predictions ŷ generated by each ofprediction combiners 520 relative to the actual values y of thepredicted variable. For example, step 908 can include calculating themean absolute percentage error (MAPE) of each prediction combiner 520using the following equation:

${MAPE}_{i} = {100 \times \frac{\sum\limits_{j = 1}^{n}{\frac{{\hat{y}}_{j} - y_{j}}{y_{j}}}}{n}\mspace{14mu} \%}$

where MAPE_(i) is the mean absolute percentage error of the ithprediction combiner 520, ŷ_(J) is the predicted value of the performancevariable for the jth sample in the evaluation period, and y_(j) is theactual value of the performance variable for the jth sample in theevaluation period. The MAPE value for a given prediction combiner 520indicates the average error of the prediction combiner 520 over theduration of the evaluation period. For example, a value of MAPE_(i)=5%indicates that the predicted values ŷ₁ . . . ŷ_(n) generated by the ithprediction combiner 520 had an average prediction error of 5% relativeto the actual values of the performance variable ŷ₁ . . . ŷ_(n) over theduration of the evaluation period.

In some embodiments, step 908 includes generating a score for each ofprediction combiners 520 based on a result of the evaluation. Forexample, step 908 can include assigning a score to each of predictioncombiners 520 based on the MAPE values for each prediction combiner 520.In some embodiments, the score is an accuracy score. Step 908 assignhigher accuracy scores to prediction combiners 520 with smaller MAPEvalues, and lower accuracy scores to prediction combiners 520 withlarger MAPE values. The accuracy scores may indicate which of predictioncombiners 520 produced the most accurate predictions, on average, overthe duration of the evaluation period.

Still referring to FIG. 9, process 900 is shown to include selecting oneof the prediction combiners based on the calculated scores (step 910).In some embodiments, step 910 is performed by combiner selector 530.Step 910 can include receiving the generated in step 908. The scores canbe MAPE scores, accuracy scores, or any other scores which indicate theprediction accuracy of prediction combiners 520. In some embodiments,step 910 includes selecting one or more of prediction combiners 520based on the assigned scores. For example, step 910 can includeselecting the prediction combiner 520 with the lowest MAPE score or thehighest accuracy score. In some embodiments, process 900 uses theselected prediction combiner 520 to generate the combined modelprediction. For example, step 910 can include activating or enabling theselected prediction combiner 520 and deactivating or disabling thenon-selected prediction combiners 520.

In some embodiments, process 900 includes periodically reactivating allof the inactive prediction combiners 520 and reevaluates theirperformance to determine whether a different prediction combiner 520 hasbecome more accurate. For example, some of prediction combiners 520 maybe more accurate under some operating conditions (e.g., high loadconditions) and less accurate under other operating conditions (e.g.,low load conditions). Process 900 can include reevaluating theperformance of each prediction combiner 520 at regular intervals or inresponse to an event (e.g., the HVAC equipment transitioning into adifferent operating mode or state) to determine whether a differentprediction combiner 520 would be more accurate than thepreviously-selected prediction combiner 520.

Process 900 is shown to include sliding the data window forward by apredetermined duration (step 912). For example, the data window can beshifted forward in time by a predetermined amount (e.g., one day) todefine a new set of training data. Step 912 is described in greaterdetail with reference to FIG. 7. After shifting the data window forward,process 900 can return to step 902. Process 900 can be repeatediteratively each time the data window is shifted.

Zone Temperature Control System

Referring now to FIG. 10, a block diagram of a temperature controlsystem 1000 is shown, according to an exemplary embodiment. System 1000is shown to include a zone controller 1002, temperature sensors 1032, abuilding zone 1034, and HVAC equipment 1036. Temperature sensors 1032measure the temperature of building zone 1034 and provide zonetemperature measurements to zone controller 1002. Zone controller 1002can use zone temperature measurements to generate control signals (e.g.,temperature setpoints, equipment operating points, etc.) for HVACequipment 1036. Zone controller 1002 can provide the control signals toHVAC equipment 1036 which operate according to the control signals toprovide heating and/or cooling to building zone 1034.

HVAC equipment 1036 can include any of a variety of HVAC equipmentoperable to control an environmental condition (e.g., temperature,humidity, etc.) in a building. For example, HVAC equipment 1036 caninclude heating devices 220, chillers 232, heat recovery heat exchangers226, cooling towers 238, thermal energy storage devices 242-244, pumps,valves, other devices of subplants 202-212, or any other type of HVACequipment or central plant equipment. Individual devices of equipment1036 can be turned on or off to adjust the amount of heating or coolingprovided to building zone 1034. In some embodiments, individual devicesof HVAC equipment 1036 can be operated at variable capacities (e.g.,operating a chiller at 10% capacity or 60% capacity) according to anoperating setpoint received from zone controller 1002, thereby affectingthe temperature of building zone 1034.

In some embodiments, zone controller 1002 uses a predictive modelingtechnique to predict the temperature of building zone 1034 at a futuretime. For example, zone controller 1002 can use a plurality of zonetemperature models 1010 to predict the temperature of building zone 1034and can use one or more prediction combiners 1020 to combine multiplezone temperature predictions to form a combined model prediction. Zonecontroller 1002 can use the combined model prediction to generate thecontrol signals for HVAC equipment 1036. Several examples of predictivemodeling techniques which can be used by zone controller 1002 aredescribed in greater detail below.

Still referring to FIG. 10, zone controller 1002 is shown to include acommunications interface 1003 and a processing circuit 1004.Communications interface 1003 may include wired or wireless interfaces(e.g., jacks, antennas, transmitters, receivers, transceivers, wireterminals, etc.) for conducting data communications with varioussystems, devices, or networks. For example, communications interface1003 may include an Ethernet card and port for sending and receivingdata via an Ethernet-based communications network and/or a WiFitransceiver for communicating via a wireless communications network.Communications interface 1003 may be configured to communicate via localarea networks or wide area networks (e.g., the Internet, a building WAN,etc.) and may use a variety of communications protocols (e.g., BACnet,IP, LON, etc.).

Communications interface 1003 may be a network interface configured tofacilitate electronic data communications between zone controller 1002and various external systems or devices (e.g., temperature sensors 1032,HVAC equipment 1036, etc.). For example, zone controller 1002 mayreceive zone temperature measurements from temperature sensors 1032 viacommunications interface 1003. In various embodiments, zone controller1002 can communicate directly with zone temperature sensors 1032 or canreceive temperature measurements via an intermediate controller orbuilding automation system (e.g., BAS 308). Zone controller 1002 can usethe zone temperature measurements to generate control signals, which canbe provided to HVAC equipment 1036 via communications interface 1003.

Processing circuit 1004 is shown to include a processor 1006 and memory1008. Processor 1006 may be a general purpose or specific purposeprocessor, an application specific integrated circuit (ASIC), one ormore field programmable gate arrays (FPGAs), a group of processingcomponents, or other suitable processing components. Processor 1006 maybe configured to execute computer code or instructions stored in memory1008 or received from other computer readable media (e.g., CDROM,network storage, a remote server, etc.).

Memory 1008 may include one or more devices (e.g., memory units, memorydevices, storage devices, etc.) for storing data and/or computer codefor completing and/or facilitating the various processes described inthe present disclosure. Memory 1008 may include random access memory(RAM), read-only memory (ROM), hard drive storage, temporary storage,non-volatile memory, flash memory, optical memory, or any other suitablememory for storing software objects and/or computer instructions. Memory1008 may include database components, object code components, scriptcomponents, or any other type of information structure for supportingthe various activities and information structures described in thepresent disclosure. Memory 1008 may be communicably connected toprocessor 1006 via processing circuit 1004 and may include computer codefor executing (e.g., by processor 1006) one or more processes describedherein.

Still referring to FIG. 10, zone controller 1006 is shown to includeseveral zone temperature models 1010. Zone temperature models 1010 caninclude any of a variety of predictive models configured to predict thetemperature of building zone 1034. In some embodiments, zone temperaturemodels 1010 predict the temperature of building zone 1034 at one or morefuture times as a function of the current (e.g., measured) zonetemperature and/or the control signals generated by temperaturecontroller 1030. Each of zone temperature models 1010 can be configuredto predict the temperature of building zone 1034 using a differentpredictive modeling technique. For example, zone temperature models 1010are shown to include state space models 1012, autoregressive models1014, and other models 1016.

State space models 1012 can use a state space model resistor capacitor(RC) network to model the temperature of building zone 1034. In someembodiments, the state space model takes the form of:

{dot over (x)}=Ax+Bu

y=Cx+Du

where x is the state vector (e.g., building mass temperatures, airtemperatures, etc.), y is the output vector (e.g., zone temperature), uis the input vector (e.g., temperature setpoints, control signals), A isthe state (or system) matrix, B is the input matrix, C is the outputmatrix, and D is the feed through (or feed forward) matrix. Zonecontroller 1002 can perform a system identification process to identifyvalues for matrices A, B, C, and D. An example of a systemidentification process which can be used by zone controller 1002 isdescribed in detail in U.S. Pat. No. 9,235,657 titled “SystemIdentification and Model Development” issued Jan. 12, 2016. The entiredisclosure of U.S. Pat. No. 9,235,657 is incorporated by referenceherein.

Autoregressive models 1014 can use an autoregressive (AR) model topredict the temperature of building zone 1034. In some embodiments, theAR model takes the form of:

y _(t) =c+ay _(t-1)+ε_(t)

where y_(t) is the temperature of building zone 1034 at time t, y_(t-1)is the temperature of building zone 1034 at time t−1, and ε_(t) isprocess noise. In some embodiments, the AR model includes a movingaverage term to provide an autoregressive moving average (ARMA) model ofthe building zone temperature. An example of an AR model which can beused by zone controller 1002 is described in detail in U.S. patentapplication Ser. No. 14/717,593 titled “Building Management System forForecasting Time Series Values of Building Variables” filed May 20,2015. The entire disclosure of U.S. patent application Ser. No.14/717,593 is incorporated by reference herein.

Each of zone temperature models 1010 can be configured to predict thetemperature of building zone 1034 using a different predictive modelingtechnique. Zone temperature models 1010 can provide the zone temperaturepredictions to prediction combiners 1020. Prediction combiners 1020 canbe configured to combine the zone temperature predictions into a singlecombined model prediction (e.g., a combined predicted temperature ofbuilding zone 1034). In some embodiments, prediction combiners 1020include multiple different prediction combiners, each of which isconfigured to combine the zone temperature predictions using a differentcombining technique. For example, prediction combiners 1020 are shown toinclude equal weighting combiner 1022, variance weighting combiner 1024,trimmed mean combiner 1026, and other combiners 1028.

Equal weighting combiner 1022 can combine multiple zone temperaturepredictions by calculating an equal-weight average of the multiple zonetemperature predictions. In some embodiments, equal weighting combiner1022 is the same or similar to equal weighting combiner 522, asdescribed with reference to FIG. 5. Variance weighting combiner 1024 cancombine multiple zone temperature predictions using a variance weightingtechnique. In some embodiments, variance weighting combiner 1024 is thesame or similar to variance weighting combiner 524, as described withreference to FIG. 5. Trimmed mean combiner 1026 can combine multiplezone temperature predictions using a trimmed mean combination technique.In some embodiments, trimmed mean combiner 1026 is the same or similarto trimmed mean combiner 526, as described with reference to FIG. 5.

Still referring to FIG. 10, zone controller 1002 is shown to include atemperature controller 1030. Temperature controller 1030 can beconfigured to generate control signals for HVAC equipment 1036 based onthe combined model prediction and/or the measured temperature ofbuilding zone 1034. In some embodiments, the control signals for HVACequipment 1036 are zone temperature setpoints. Temperature controller1030 can use a model predictive control (MPC) technique to generate thezone temperature setpoints for each time step during an optimizationperiod. In some embodiments, temperature controller 1030 performs anoptimization process to generate zone temperature setpoints whichminimize power consumption and/or energy cost over the optimizationperiod.

In some embodiments, temperature controller 1030 performs the setpointoptimization subject to constraints on the temperature of building zone1034, equipment capacities, and/or other optimization constraints.Temperature controller 1030 can use the combined model prediction fromprediction combiners 1020 to determine the temperature of building zone1034 predicted to result from a given set of temperature setpoints.Temperature controller 1030 can generate the zone temperature setpointssuch that the combined model prediction (e.g., the predicted temperatureof building zone 1034) is maintained within a predetermined temperaturerange.

Temperature controller 1030 can provide the control signals to HVACequipment 1036. HVAC equipment 1036 operate according to the controlsignals to adjust an amount of heating or cooling provided to buildingzone 1034. For example, HVAC equipment 1036 can include heaters,chillers, fans, or other types of HVAC equipment configured to provideheating or cooling to building zone 1034. By operating HVAC equipment1036, zone controller 1002 can affect the temperature or otherenvironmental conditions of building zone 1034. Temperature controller1036 can also provide the control signals to zone temperature models1010. In some embodiments, zone temperature models 1010 use the controlsignals in combination with the current (e.g., measured) zonetemperature to generate the zone temperature predictions.

Predictive modeling system 402 and temperature control system 1000 areexamples of systems which use the model combining techniques describedherein to generate a combined model prediction. However, it should beunderstood that the model combining techniques are not limited topredictive models. The model combining techniques can also be used tocombine the outputs of non-predictive models to form a combined modeloutput. For example, various types of non-predictive modeling systemscan use the model combining techniques to generate a combined estimatefor a variable of interest. One example of such a non-predictivemodeling system is load estimation system 1100, described in detailbelow.

Load Estimation System

Referring now to FIGS. 11-12, load estimation system 1100 is shown,according to an exemplary embodiment. Load estimation system 1100 is anexample of a non-predictive modeling system which can use the modelcombining techniques described herein to generate a combined estimatefor a variable of interest (e.g., a combined load estimate). System 1100is shown to include central plant controller 302 and a load estimator1102. Central plant controller 302 can be configured to monitor andcontrol central plant 200, as described with reference to FIG. 3. Insome embodiments, central plant controller 302 requires hourly heatingand cooling loads as inputs. However, the heating and cooling load datamay only be available in longer intervals (e.g., monthly heating loadsand daily cooling loads). In the event that heating and cooling loaddata are not available in hourly intervals, load estimator 1102 candisaggregate the load data for longer intervals to generate the requiredinputs for central plant controller 302.

Load estimator 1102 may receive inputs of cumulative building energyloads over a first time period (e.g., monthly heating loads and dailycooling loads). Load estimator 1102 may increase the resolution of thecumulative building energy loads to generate load values for each of aplurality of second time periods shorter than the first time period. Forexample, load estimator 1102 may transform the monthly heating loads anddaily cooling loads into hourly heating and cooling loads and mayprovide the hourly load values to central plant controller 302. Centralplant controller 302 may control operations of central plant 200 usingthe hourly heating and cooling loads.

Load estimator 1102 is shown to receive inputs of monthly heating anddaily cooling loads, according to an exemplary embodiment. The timeperiod over which each of the loads may be sampled is not limited tothose shown or specifically enumerated, and may be any amount of time.For example, the time period may be a month for cooling loads and a dayfor heating loads. In some embodiments, the time periods are measured inminutes or seconds. In some embodiments, load estimator 1102 receivesonly heating loads or only cooling loads. In other embodiments loadestimator 1102 receives both heating and cooling loads. In someembodiments, the building energy loads are sampled by load estimator1102 directly from plant equipment. In other embodiments, the buildingenergy loads are input to load estimator 1102 from utility providers oran outside source, such as a third-party utility management system.

Load estimator 1102 may receive inputs of hourly predictor variablevalues, according to an exemplary embodiment. Predictor variables may bedirectly correlated to the load on central plant 200. Properly selectedpredictor variables are important to accurately estimate building energyloads. Although hourly values for the predictor variables are shown inFIG. 11, it should be understood that the time period over or intervalat which each of the predictor variables is sampled is not limited tothose shown or specifically enumerated, and may be any length of time.For example, the sampling interval could be five minutes, three hours,or any other duration. The resolution at which each of the predictorvariables is sampled may be the same as the resolution of the loadvalues estimated by load estimator 1102. For example, if load estimator1102 estimates hourly building energy loads, load estimator 1102 mayreceive hourly predictor variable values.

Using the sampled predictor variable values, load estimator 1102 maygenerate a model that estimates the building energy load in terms of(i.e., as a function of) the predictor variables. After the model istrained, load estimator 1102 may use the model to estimate buildingenergy loads over a plurality of time periods. For example, loadestimator 1102 may estimate hourly cooling loads over a day. Theestimated building energy loads may be estimated for time periods withinthe time period of the received building energy load. For example, loadestimator 1102 may receive a monthly heating load. Load estimator 1102may estimate hourly heating loads over the same month for which themonthly heating load was received. The input load data may include aplurality of data points. In some embodiments, the number of input loaddata points is preferably equal to, or greater than, the number ofpredictor variables.

The estimated building energy loads may be transmitted to central plantcontroller 302. Central plant controller 302 may use the estimatedbuilding energy loads to make control decisions for central plant 200.For example, central plant controller 302 may control a distribution ofenergy loads in central plant 200 based on the estimated building energyloads, as described with reference to FIG. 3. In some embodiments, loadestimator 1102 includes some or all of the features of the loadestimator described in U.S. patent application Ser. No. 14/971,813 filedDec. 16, 2015, the entire disclosure of which is incorporated byreference herein.

Referring now to FIG. 12, a block diagram illustrating load estimator1102 in greater detail is shown, according to an exemplary embodiment.Load estimator 1102 may receive one or more cumulative building energyloads (e.g., heating or cooling loads) for a first time period. Forexample, load estimator 1102 is shown receiving a monthly heating loadand a daily cooling load. The time period over which each of the loadsmay be sampled is not limited to those shown or specifically enumerated,and may be any amount of time. Load estimator 1102 may be configured toincrease the resolution of the building energy loads and providehigher-resolution building energy loads to central plant controller 302.For example, load estimator 1102 may transform the monthly heating loadinto hourly heating load values for each hour in the first time period(e.g., each hour in the month for which the cumulative heating load isreceived). Similarly, load estimator 1102 may transform the dailycooling load into hourly cooling load values for each hour in the firsttime period (e.g., each hour in the day for which the cumulative coolingload is received). Load estimator 1102 may provide the hourly heatingand cooling load values to central plant controller 302 for use inoptimizing central plant operation.

Load estimator 1102 is shown to include a processing circuit 1104 and acommunications interface 1103. Communications interface 1103 may includewired or wireless interfaces (e.g., jacks, antennas, transmitters,receivers, transceivers, wire terminals, etc.) for conducting datacommunications with various systems, devices, or networks. For example,communications interface 1103 may include an Ethernet card and port forsending and receiving data via an Ethernet-based communications networkand/or a Wi-Fi transceiver for communicating via a wirelesscommunications network. Communications interface 1103 may be configuredto communicate via local area networks or wide area networks (e.g., theInternet, a building WAN, etc.) and may use a variety of communicationsprotocols (e.g., BACnet, IP, LON, etc.).

Communications interface 1103 may be a network interface configured tofacilitate electronic data communications between load estimator 1102and various external systems or devices (e.g., central plant controller302, BAS 308, central plant 200, etc.). For example, load estimator 1202may receive information from central plant controller 302 indicating oneor more measured states of the controlled building (e.g., temperature,humidity, electric loads, etc.) and one or more states of equipment 340(e.g., equipment status, power consumption, equipment availability,etc.). Communications interface 1103 may receive inputs from BAS 308and/or equipment 340 and may provide operating parameters (e.g., on/offdecisions, setpoints, etc.) to equipment 340 via BAS 308. The operatingparameters may cause BAS 308 to activate, deactivate, or adjust asetpoint for various devices of equipment 340.

Processing circuit 1104 is shown to include a processor 1106 and memory1108. Processor 1106 may be a general purpose or specific purposeprocessor, an application specific integrated circuit (ASIC), one ormore field programmable gate arrays (FPGAs), a group of processingcomponents, or other suitable processing components. Processor 1106 maybe configured to execute computer code or instructions stored in memory1108 or received from other computer readable media (e.g., CDROM,network storage, a remote server, etc.).

Memory 1108 may include one or more devices (e.g., memory units, memorydevices, storage devices, etc.) for storing data and/or computer codefor completing and/or facilitating the various processes described inthe present disclosure. Memory 1108 may include random access memory(RAM), read-only memory (ROM), hard drive storage, temporary storage,non-volatile memory, flash memory, optical memory, or any other suitablememory for storing software objects and/or computer instructions. Memory1108 may include database components, object code components, scriptcomponents, or any other type of information structure for supportingthe various activities and information structures described in thepresent disclosure. Memory 1108 may be communicably connected toprocessor 1106 via processing circuit 1104 and may include computer codefor executing (e.g., by processor 1106) one or more processes describedherein.

Still referring to FIG. 12, load estimator 1102 is shown to includeseveral load models 1110. Load models 1110 can include any of a varietyof models configured to estimate hourly heating or cooling loads. Insome embodiments, load models 1110 estimate the heating and coolingloads at hourly intervals as a function of the monthly heating load, thedaily cooling load, and/or the hourly predictor variable values. Each ofload models 1110 can be configured to estimate the heating and coolingloads using a different modeling technique. For example, load models1110 are shown to include model 1, model 2, . . . , model N, where N isthe total number of load models 1110. Each of the N load models 1110 canhave a different model form, or otherwise implement a different modelingtechnique to estimate the heating and cooling loads.

Each of load models 1110 can generate a set of hourly load estimates.Each set of hourly load estimates can include multiple hourly loadestimates (e.g., a load estimate for each hour). Load models 1110 canprovide the hourly load estimates to estimate combiners 1120. Estimatecombiners 1120 can be configured to combine the hourly load estimatesinto a single combined set of hourly load estimates (e.g., a combinedload estimate for each hour). In some embodiments, estimate combiners1120 include multiple different estimate combiners, each of which isconfigured to combine the hourly load estimates using a differentcombining technique. For example, estimate combiners 1120 are shown toinclude equal weighting combiner 1122, variance weighting combiner 1124,and trimmed mean combiner 1126.

Equal weighting combiner 1122 can combine multiple sets of hourly loadestimates by calculating an equal-weight average of the hourly loadestimates for each hour. In some embodiments, equal weighting combiner1122 is the same or similar to equal weighting combiner 522, asdescribed with reference to FIG. 5. Variance weighting combiner 1124 cancombine multiple sets of hourly load estimates using a varianceweighting technique. In some embodiments, variance weighting combiner1124 is the same or similar to variance weighting combiner 524, asdescribed with reference to FIG. 5. Trimmed mean combiner 1126 cancombine multiple sets of hourly load estimates using a trimmed meancombination technique. In some embodiments, trimmed mean combiner 1126is the same or similar to trimmed mean combiner 526, as described withreference to FIG. 5. The combined hourly load estimates can be providedto central plant controller 302 and used to optimize the performance ofcentral plant 200.

Configuration of Exemplary Embodiments

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements can bereversed or otherwise varied and the nature or number of discreteelements or positions can be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepscan be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions can be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure can be implementedusing existing computer processors, or by a special purpose computerprocessor for an appropriate system, incorporated for this or anotherpurpose, or by a hardwired system. Embodiments within the scope of thepresent disclosure include program products comprising machine-readablemedia for carrying or having machine-executable instructions or datastructures stored thereon. Such machine-readable media can be anyavailable media that can be accessed by a general purpose or specialpurpose computer or other machine with a processor. By way of example,such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROMor other optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to carry or storedesired program code in the form of machine-executable instructions ordata structures and which can be accessed by a general purpose orspecial purpose computer or other machine with a processor. Combinationsof the above are also included within the scope of machine-readablemedia. Machine-executable instructions include, for example,instructions and data which cause a general purpose computer, specialpurpose computer, or special purpose processing machines to perform acertain function or group of functions.

Although the figures show a specific order of method steps, the order ofthe steps may differ from what is depicted. Also two or more steps canbe performed concurrently or with partial concurrence. Such variationwill depend on the software and hardware systems chosen and on designerchoice. All such variations are within the scope of the disclosure.Likewise, software implementations could be accomplished with standardprogramming techniques with rule based logic and other logic toaccomplish the various connection steps, processing steps, comparisonsteps and decision steps.

What is claimed is:
 1. A heating, ventilation, or air conditioning(HVAC) system for a building, the HVAC system comprising: HVAC equipmentoperable to affect an environmental condition in the building; acontroller configured to determine an operating point for the HVACequipment and to operate the HVAC equipment at the operating point; anda predictive modeling system comprising: a plurality of HVAC componentmodels configured to generate a plurality of component model predictionsbased on the operating point, wherein each of the component modelpredictions is generated by one of the HVAC component models andcomprises a predicted value of a performance variable indicating apredicted performance of the HVAC equipment at the operating point; andone or more prediction combiners configured to combine the plurality ofcomponent model predictions to form a combined model prediction, whereinthe combined model prediction comprises another predicted value of theperformance variable; wherein the controller is configured to use thecombined model prediction to optimize the operating point and to operatethe HVAC equipment at the optimized operating point.
 2. The HVAC systemof claim 1, wherein the operating point is a setpoint for the HVACequipment and the performance variable indicates a predicted powerconsumption of the HVAC equipment at the setpoint.
 3. The HVAC system ofclaim 1, further comprising one or more sensors configured to measureone or more measured variables associated with the HVAC equipment;wherein the HVAC component models are configured to generate thecomponent model predictions as a function of the measured variables. 4.The HVAC system of claim 1, wherein each of the HVAC component modelshas a different functional form and uses a different mathematicalrelationship to generate the corresponding component model prediction.5. The HVAC system of claim 1, wherein the prediction combiners comprisean equal weighting combiner configured to generate the combined modelprediction by calculating an average of the component model predictions.6. The HVAC system of claim 1, wherein the prediction combiners comprisea variance weighting combiner configured to: identify a varianceassociated with each of the component model predictions; assign a weightto each of the component model predictions based on the varianceassociated therewith; and generate the combined model prediction bycalculating a weighted average of the component model predictions usingthe assigned weights.
 7. The HVAC system of claim 1, wherein theprediction combiners comprise a trimmed mean combiner configured to:create an initial set of the component model predictions; identify oneor more highest values of the component model predictions and one ormore lowest values of the component model predictions; create a filteredsubset of the component model predictions by removing the identifiedcomponent model predictions from the initial set; and generate thecombined model prediction by calculating an average of the componentmodel predictions in the filtered subset.
 8. The HVAC system of claim 7,wherein the trimmed mean combiner is configured to use a varianceweighting technique to calculate the average of the component modelpredictions in the filtered subset, the variance weighting techniquecomprising: identifying a variance associated with each of the componentmodel predictions in the filtered subset; assigning a weight to each ofthe component model predictions based on the variance associatedtherewith; and generating the combined model prediction by calculating aweighted average of the component model predictions in the filteredsubset using the assigned weights.
 9. The HVAC system of claim 1,further comprising: a model evaluator configured to calculate a scorefor each of the prediction combiners by comparing the combined modelpredictions generated by each of the prediction combiners to actualvalues of the performance variable; and a combiner selector configureduse the calculated scores to select one of the prediction combiners;wherein the predictive modeling system is configured to use the selectedprediction combiner to generate the combined model prediction.
 10. Aheating, ventilation, or air conditioning (HVAC) system for a building,the HVAC system comprising: HVAC equipment operable to affect atemperature of the building; a plurality of zone temperature modelsconfigured to generate a plurality of zone temperature predictions,wherein each of the zone temperature predictions is generated by one ofthe zone temperature models and comprises a predicted value of thetemperature of the building; one or more prediction combiners configuredto combine the plurality of zone temperature predictions to form acombined model prediction, wherein the combined model predictioncomprises another predicted value of the temperature of the building; atemperature controller configured to use the combined model predictionto generate control signals for the HVAC equipment and to operate theHVAC equipment according to the control signals.
 11. The HVAC system ofclaim 10, further comprising one or more sensors configured to measurethe temperature of the building; wherein the zone temperature models areconfigured to generate the zone temperature predictions as a function ofthe measured temperature of the building and the control signals for theHVAC equipment.
 12. The HVAC system of claim 10, wherein the predictioncombiners comprise a variance weighting combiner configured to: identifya variance associated with each of the zone temperature predictions;assign a weight to each of the zone temperature predictions based on thevariance associated therewith; and generate the combined modelprediction by calculating a weighted average of the zone temperaturepredictions using the assigned weights.
 13. The HVAC system of claim 10,wherein the prediction combiners comprise a trimmed mean combinerconfigured to: create an initial set of the zone temperaturepredictions; identify one or more highest values of the zone temperaturepredictions and one or more lowest values of the zone temperaturepredictions; create a filtered subset of the zone temperaturepredictions by removing the identified zone temperature predictions fromthe initial set; and generate the combined model prediction bycalculating an average of the zone temperature predictions in thefiltered subset.
 14. The HVAC system of claim 10, further comprising: amodel evaluator configured to calculate a score for each of theprediction combiners by comparing the combined model predictionsgenerated by each of the prediction combiners to actual values of thetemperature of the building; and a combiner selector configured use thecalculated scores to select one of the prediction combiners; wherein theselected prediction combiner is used to generate the combined modelprediction.
 15. A heating, ventilation, or air conditioning (HVAC)system for a building, the HVAC system comprising: HVAC equipmentoperable to affect a temperature of the building; a plurality of modelsconfigured to estimate a plurality of values for a variable of interestin the HVAC system, wherein each of the plurality of values is estimatedby one of the plurality of models; one or more estimate combinersconfigured to combine the plurality of estimated values to form acombined model estimate, wherein the combined model estimate comprisesanother value of the variable of interest; a controller configured touse the combined model estimate to generate control signals for the HVACequipment and to operate the HVAC equipment according to the controlsignals.
 16. The HVAC system of claim 15, further comprising one or moresensors configured to measure one or more predictor variables; whereinthe plurality of models are configured to estimate the variable ofinterest as a function of the measured predictor variables.
 17. The HVACsystem of claim 16, wherein: the variable of interest is a buildingenergy load; each of the plurality of models is configured to estimate avalue for the building energy load at each of a plurality of timeswithin a time period; and the predictor variables comprise one or morevariables that affect the building energy load during the time period.18. The HVAC system of claim 15, wherein the estimate combiners comprisea variance weighting combiner configured to: identify a varianceassociated with each of the estimated values generated by the pluralityof models; assign a weight to each of the estimated values based on thevariance associated therewith; and generate the combined model estimateby calculating a weighted average of the estimated values using theassigned weights.
 19. The HVAC system of claim 15, wherein the estimatecombiners comprise a trimmed mean combiner configured to: create aninitial set of the estimated values generated by the plurality ofmodels; identify one or more highest values of the estimated values andone or more lowest values of the estimated values; create a filteredsubset of the estimated values by removing the identified estimatedvalues from the initial set; and generate the combined model estimate bycalculating an average of the estimated values in the filtered subset.20. The HVAC system of claim 15, further comprising: a model evaluatorconfigured to calculate a score for each of the estimate combiners bycomparing the combined model estimates generated by each of the estimatecombiners to actual values of the variable of interest; and a combinerselector configured use the calculated scores to select one of theestimate combiners; wherein the selected estimate combiner is used togenerate the combined model estimate.